Line arrangements and configurations of points with an unexpected geometric property
We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union X of fat points imposes on the complete linear system of curves in P-2 of fixed degree d, in terms of the occurrence of certa...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Cook, David W. [verfasserIn] Harbourne, Brian - 1955- [verfasserIn] Migliore, Juan C. - 1956- [verfasserIn] Nagel, Uwe [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2018 |
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| Ausgabe: |
Published online by Cambridge University Press: 10 September 2018 |
| Schlagwörter: |
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| Anmerkung: |
Last seen: 02.11.2022 |
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| Übergeordnetes Werk: |
Enthalten in: Compositio mathematica - Cambridge : Cambridge Univ. Press, 1935, Volume 154(2018), Issue 10, pp. 2150-2194 |
|---|---|
| Übergeordnetes Werk: |
volume:154 ; year:2018 ; number:10 ; pages:2150-2194 |
| Links: |
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| DOI / URN: |
10.1112/S0010437X18007376 |
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| Katalog-ID: |
1820523799 |
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| 245 | 1 | 0 | |a Line arrangements and configurations of points with an unexpected geometric property |
| 250 | |a Published online by Cambridge University Press: 10 September 2018 | ||
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| 520 | |a We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union X of fat points imposes on the complete linear system of curves in P-2 of fixed degree d, in terms of the occurrence of certain rational curves in the base locus of the linear subsystem defined by X. As a first step towards a new theory, we show that rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points. Moreover, motivated by work of Di Gennaro, Ilardi and Valles and of Faenzi and Valles, we relate our results to the failure of a strong Lefschetz property, and we give a Lefschetz-like criterion for Terao's conjecture on the freeness of line arrangements. | ||
| 650 | 4 | |a Unexpected curves | |
| 650 | 4 | |a Fat points | |
| 650 | 4 | |a Line arrangements | |
| 650 | 4 | |a Strong Lefschetz property | |
| 650 | 4 | |a Linear systems | |
| 650 | 4 | |a Stable vector bundle | |
| 650 | 4 | |a Splitting type | |
| 700 | 1 | |a Harbourne, Brian |d 1955- |e verfasserin |0 (DE-588)172125529 |0 (DE-627)697039129 |0 (DE-576)132997908 |4 aut | |
| 700 | 1 | |a Migliore, Juan C. |d 1956- |e verfasserin |0 (DE-588)120495252 |0 (DE-627)69672538X |0 (DE-576)319430995 |4 aut | |
| 700 | 1 | |a Nagel, Uwe |e verfasserin |0 (DE-588)1153416387 |0 (DE-627)1014828090 |0 (DE-576)500214719 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Compositio mathematica |d Cambridge : Cambridge Univ. Press, 1935 |g Volume 154(2018), Issue 10, pp. 2150-2194 |h Online-Ressource |w (DE-627)266882692 |w (DE-600)1468114-6 |w (DE-576)102668906 |x 1570-5846 |7 nnns |
| 773 | 1 | 8 | |g volume:154 |g year:2018 |g number:10 |g pages:2150-2194 |
| 856 | 4 | 0 | |u https://doi.org/10.1112/S0010437X18007376 |x Verlag |x Resolving-System |y Full text at Publisher |z lizenzpflichtig |
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| 952 | |d 154 |j 2018 |e 10 |h 2150-2194 |y Volume 154(2018), Issue 10, pp. 2150-2194 | ||
| 980 | |2 2088 |1 01 |x DE-Frei3c |b 4205749902 |c 00 |f --%%-- |d --%%-- |e --%%-- |j --%%-- |k Funding text: [...]We also thank the Mathematisches Forschunginstitut Oberwolfach and the Banff International Research Station for supporting the workshops which gave us the opportunity to discuss and present our results.[...] |y l01 |z 02-11-22 | ||
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10.1112/S0010437X18007376 doi (DE-627)1820523799 (DE-599)KXP1820523799 DE-627 ger DE-627 rda eng 14N20 msc 13D02 msc 14C20 msc 14N05 msc 05E40 msc 14F05 msc Cook, David W. verfasserin aut Line arrangements and configurations of points with an unexpected geometric property Published online by Cambridge University Press: 10 September 2018 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 02.11.2022 We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union X of fat points imposes on the complete linear system of curves in P-2 of fixed degree d, in terms of the occurrence of certain rational curves in the base locus of the linear subsystem defined by X. As a first step towards a new theory, we show that rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points. Moreover, motivated by work of Di Gennaro, Ilardi and Valles and of Faenzi and Valles, we relate our results to the failure of a strong Lefschetz property, and we give a Lefschetz-like criterion for Terao's conjecture on the freeness of line arrangements. Unexpected curves Fat points Line arrangements Strong Lefschetz property Linear systems Stable vector bundle Splitting type Harbourne, Brian 1955- verfasserin (DE-588)172125529 (DE-627)697039129 (DE-576)132997908 aut Migliore, Juan C. 1956- verfasserin (DE-588)120495252 (DE-627)69672538X (DE-576)319430995 aut Nagel, Uwe verfasserin (DE-588)1153416387 (DE-627)1014828090 (DE-576)500214719 aut Enthalten in Compositio mathematica Cambridge : Cambridge Univ. Press, 1935 Volume 154(2018), Issue 10, pp. 2150-2194 Online-Ressource (DE-627)266882692 (DE-600)1468114-6 (DE-576)102668906 1570-5846 nnns volume:154 year:2018 number:10 pages:2150-2194 https://doi.org/10.1112/S0010437X18007376 Verlag Resolving-System Full text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2089 GBV_ILN_2093 GBV_ILN_2098 GBV_ILN_2107 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2145 GBV_ILN_2158 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2924 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 154 2018 10 2150-2194 Volume 154(2018), Issue 10, pp. 2150-2194 2088 01 DE-Frei3c 4205749902 00 --%%-- --%%-- --%%-- --%%-- Funding text: [...]We also thank the Mathematisches Forschunginstitut Oberwolfach and the Banff International Research Station for supporting the workshops which gave us the opportunity to discuss and present our results.[...] l01 02-11-22 2088 01 DE-Frei3c 00 (DE-627)1294695886 AMS:14 Algebraic geometry 2088 01 DE-Frei3c 00 (DE-627)1294691201 AMS:13 Commutative rings and algebras 2088 01 DE-Frei3c 00 (DE-627)1294696033 AMS:05 Combinatorics |
| spelling |
10.1112/S0010437X18007376 doi (DE-627)1820523799 (DE-599)KXP1820523799 DE-627 ger DE-627 rda eng 14N20 msc 13D02 msc 14C20 msc 14N05 msc 05E40 msc 14F05 msc Cook, David W. verfasserin aut Line arrangements and configurations of points with an unexpected geometric property Published online by Cambridge University Press: 10 September 2018 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 02.11.2022 We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union X of fat points imposes on the complete linear system of curves in P-2 of fixed degree d, in terms of the occurrence of certain rational curves in the base locus of the linear subsystem defined by X. As a first step towards a new theory, we show that rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points. Moreover, motivated by work of Di Gennaro, Ilardi and Valles and of Faenzi and Valles, we relate our results to the failure of a strong Lefschetz property, and we give a Lefschetz-like criterion for Terao's conjecture on the freeness of line arrangements. Unexpected curves Fat points Line arrangements Strong Lefschetz property Linear systems Stable vector bundle Splitting type Harbourne, Brian 1955- verfasserin (DE-588)172125529 (DE-627)697039129 (DE-576)132997908 aut Migliore, Juan C. 1956- verfasserin (DE-588)120495252 (DE-627)69672538X (DE-576)319430995 aut Nagel, Uwe verfasserin (DE-588)1153416387 (DE-627)1014828090 (DE-576)500214719 aut Enthalten in Compositio mathematica Cambridge : Cambridge Univ. Press, 1935 Volume 154(2018), Issue 10, pp. 2150-2194 Online-Ressource (DE-627)266882692 (DE-600)1468114-6 (DE-576)102668906 1570-5846 nnns volume:154 year:2018 number:10 pages:2150-2194 https://doi.org/10.1112/S0010437X18007376 Verlag Resolving-System Full text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2089 GBV_ILN_2093 GBV_ILN_2098 GBV_ILN_2107 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2145 GBV_ILN_2158 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2924 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 154 2018 10 2150-2194 Volume 154(2018), Issue 10, pp. 2150-2194 2088 01 DE-Frei3c 4205749902 00 --%%-- --%%-- --%%-- --%%-- Funding text: [...]We also thank the Mathematisches Forschunginstitut Oberwolfach and the Banff International Research Station for supporting the workshops which gave us the opportunity to discuss and present our results.[...] l01 02-11-22 2088 01 DE-Frei3c 00 (DE-627)1294695886 AMS:14 Algebraic geometry 2088 01 DE-Frei3c 00 (DE-627)1294691201 AMS:13 Commutative rings and algebras 2088 01 DE-Frei3c 00 (DE-627)1294696033 AMS:05 Combinatorics |
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10.1112/S0010437X18007376 doi (DE-627)1820523799 (DE-599)KXP1820523799 DE-627 ger DE-627 rda eng 14N20 msc 13D02 msc 14C20 msc 14N05 msc 05E40 msc 14F05 msc Cook, David W. verfasserin aut Line arrangements and configurations of points with an unexpected geometric property Published online by Cambridge University Press: 10 September 2018 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 02.11.2022 We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union X of fat points imposes on the complete linear system of curves in P-2 of fixed degree d, in terms of the occurrence of certain rational curves in the base locus of the linear subsystem defined by X. As a first step towards a new theory, we show that rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points. Moreover, motivated by work of Di Gennaro, Ilardi and Valles and of Faenzi and Valles, we relate our results to the failure of a strong Lefschetz property, and we give a Lefschetz-like criterion for Terao's conjecture on the freeness of line arrangements. Unexpected curves Fat points Line arrangements Strong Lefschetz property Linear systems Stable vector bundle Splitting type Harbourne, Brian 1955- verfasserin (DE-588)172125529 (DE-627)697039129 (DE-576)132997908 aut Migliore, Juan C. 1956- verfasserin (DE-588)120495252 (DE-627)69672538X (DE-576)319430995 aut Nagel, Uwe verfasserin (DE-588)1153416387 (DE-627)1014828090 (DE-576)500214719 aut Enthalten in Compositio mathematica Cambridge : Cambridge Univ. Press, 1935 Volume 154(2018), Issue 10, pp. 2150-2194 Online-Ressource (DE-627)266882692 (DE-600)1468114-6 (DE-576)102668906 1570-5846 nnns volume:154 year:2018 number:10 pages:2150-2194 https://doi.org/10.1112/S0010437X18007376 Verlag Resolving-System Full text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2089 GBV_ILN_2093 GBV_ILN_2098 GBV_ILN_2107 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2145 GBV_ILN_2158 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2924 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 154 2018 10 2150-2194 Volume 154(2018), Issue 10, pp. 2150-2194 2088 01 DE-Frei3c 4205749902 00 --%%-- --%%-- --%%-- --%%-- Funding text: [...]We also thank the Mathematisches Forschunginstitut Oberwolfach and the Banff International Research Station for supporting the workshops which gave us the opportunity to discuss and present our results.[...] l01 02-11-22 2088 01 DE-Frei3c 00 (DE-627)1294695886 AMS:14 Algebraic geometry 2088 01 DE-Frei3c 00 (DE-627)1294691201 AMS:13 Commutative rings and algebras 2088 01 DE-Frei3c 00 (DE-627)1294696033 AMS:05 Combinatorics |
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10.1112/S0010437X18007376 doi (DE-627)1820523799 (DE-599)KXP1820523799 DE-627 ger DE-627 rda eng 14N20 msc 13D02 msc 14C20 msc 14N05 msc 05E40 msc 14F05 msc Cook, David W. verfasserin aut Line arrangements and configurations of points with an unexpected geometric property Published online by Cambridge University Press: 10 September 2018 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 02.11.2022 We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union X of fat points imposes on the complete linear system of curves in P-2 of fixed degree d, in terms of the occurrence of certain rational curves in the base locus of the linear subsystem defined by X. As a first step towards a new theory, we show that rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points. Moreover, motivated by work of Di Gennaro, Ilardi and Valles and of Faenzi and Valles, we relate our results to the failure of a strong Lefschetz property, and we give a Lefschetz-like criterion for Terao's conjecture on the freeness of line arrangements. Unexpected curves Fat points Line arrangements Strong Lefschetz property Linear systems Stable vector bundle Splitting type Harbourne, Brian 1955- verfasserin (DE-588)172125529 (DE-627)697039129 (DE-576)132997908 aut Migliore, Juan C. 1956- verfasserin (DE-588)120495252 (DE-627)69672538X (DE-576)319430995 aut Nagel, Uwe verfasserin (DE-588)1153416387 (DE-627)1014828090 (DE-576)500214719 aut Enthalten in Compositio mathematica Cambridge : Cambridge Univ. Press, 1935 Volume 154(2018), Issue 10, pp. 2150-2194 Online-Ressource (DE-627)266882692 (DE-600)1468114-6 (DE-576)102668906 1570-5846 nnns volume:154 year:2018 number:10 pages:2150-2194 https://doi.org/10.1112/S0010437X18007376 Verlag Resolving-System Full text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2089 GBV_ILN_2093 GBV_ILN_2098 GBV_ILN_2107 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2145 GBV_ILN_2158 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2924 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 154 2018 10 2150-2194 Volume 154(2018), Issue 10, pp. 2150-2194 2088 01 DE-Frei3c 4205749902 00 --%%-- --%%-- --%%-- --%%-- Funding text: [...]We also thank the Mathematisches Forschunginstitut Oberwolfach and the Banff International Research Station for supporting the workshops which gave us the opportunity to discuss and present our results.[...] l01 02-11-22 2088 01 DE-Frei3c 00 (DE-627)1294695886 AMS:14 Algebraic geometry 2088 01 DE-Frei3c 00 (DE-627)1294691201 AMS:13 Commutative rings and algebras 2088 01 DE-Frei3c 00 (DE-627)1294696033 AMS:05 Combinatorics |
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10.1112/S0010437X18007376 doi (DE-627)1820523799 (DE-599)KXP1820523799 DE-627 ger DE-627 rda eng 14N20 msc 13D02 msc 14C20 msc 14N05 msc 05E40 msc 14F05 msc Cook, David W. verfasserin aut Line arrangements and configurations of points with an unexpected geometric property Published online by Cambridge University Press: 10 September 2018 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 02.11.2022 We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union X of fat points imposes on the complete linear system of curves in P-2 of fixed degree d, in terms of the occurrence of certain rational curves in the base locus of the linear subsystem defined by X. As a first step towards a new theory, we show that rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points. Moreover, motivated by work of Di Gennaro, Ilardi and Valles and of Faenzi and Valles, we relate our results to the failure of a strong Lefschetz property, and we give a Lefschetz-like criterion for Terao's conjecture on the freeness of line arrangements. Unexpected curves Fat points Line arrangements Strong Lefschetz property Linear systems Stable vector bundle Splitting type Harbourne, Brian 1955- verfasserin (DE-588)172125529 (DE-627)697039129 (DE-576)132997908 aut Migliore, Juan C. 1956- verfasserin (DE-588)120495252 (DE-627)69672538X (DE-576)319430995 aut Nagel, Uwe verfasserin (DE-588)1153416387 (DE-627)1014828090 (DE-576)500214719 aut Enthalten in Compositio mathematica Cambridge : Cambridge Univ. Press, 1935 Volume 154(2018), Issue 10, pp. 2150-2194 Online-Ressource (DE-627)266882692 (DE-600)1468114-6 (DE-576)102668906 1570-5846 nnns volume:154 year:2018 number:10 pages:2150-2194 https://doi.org/10.1112/S0010437X18007376 Verlag Resolving-System Full text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2089 GBV_ILN_2093 GBV_ILN_2098 GBV_ILN_2107 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2145 GBV_ILN_2158 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2924 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 154 2018 10 2150-2194 Volume 154(2018), Issue 10, pp. 2150-2194 2088 01 DE-Frei3c 4205749902 00 --%%-- --%%-- --%%-- --%%-- Funding text: [...]We also thank the Mathematisches Forschunginstitut Oberwolfach and the Banff International Research Station for supporting the workshops which gave us the opportunity to discuss and present our results.[...] l01 02-11-22 2088 01 DE-Frei3c 00 (DE-627)1294695886 AMS:14 Algebraic geometry 2088 01 DE-Frei3c 00 (DE-627)1294691201 AMS:13 Commutative rings and algebras 2088 01 DE-Frei3c 00 (DE-627)1294696033 AMS:05 Combinatorics |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a2200265 4500</leader><controlfield tag="001">1820523799</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20221102161654.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">221102s2018 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1112/S0010437X18007376</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)1820523799</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)KXP1820523799</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">14N20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">13D02</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">14C20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">14N05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">05E40</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">14F05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Cook, David W.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Line arrangements and configurations of points with an unexpected geometric property</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Published online by Cambridge University Press: 10 September 2018</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Last seen: 02.11.2022</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union X of fat points imposes on the complete linear system of curves in P-2 of fixed degree d, in terms of the occurrence of certain rational curves in the base locus of the linear subsystem defined by X. As a first step towards a new theory, we show that rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points. Moreover, motivated by work of Di Gennaro, Ilardi and Valles and of Faenzi and Valles, we relate our results to the failure of a strong Lefschetz property, and we give a Lefschetz-like criterion for Terao's conjecture on the freeness of line arrangements.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Unexpected curves</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fat points</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Line arrangements</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Strong Lefschetz property</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linear systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stable vector bundle</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Splitting type</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Harbourne, Brian</subfield><subfield code="d">1955-</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(DE-588)172125529</subfield><subfield code="0">(DE-627)697039129</subfield><subfield code="0">(DE-576)132997908</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Migliore, Juan C.</subfield><subfield code="d">1956-</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(DE-588)120495252</subfield><subfield code="0">(DE-627)69672538X</subfield><subfield code="0">(DE-576)319430995</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Nagel, Uwe</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(DE-588)1153416387</subfield><subfield code="0">(DE-627)1014828090</subfield><subfield code="0">(DE-576)500214719</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Compositio mathematica</subfield><subfield code="d">Cambridge : Cambridge Univ. 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Cook, David W. msc 14N20 msc 13D02 msc 14C20 msc 14N05 msc 05E40 msc 14F05 misc Unexpected curves misc Fat points misc Line arrangements misc Strong Lefschetz property misc Linear systems misc Stable vector bundle misc Splitting type Line arrangements and configurations of points with an unexpected geometric property |
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14N20 msc 13D02 msc 14C20 msc 14N05 msc 05E40 msc 14F05 msc Line arrangements and configurations of points with an unexpected geometric property Unexpected curves Fat points Line arrangements Strong Lefschetz property Linear systems Stable vector bundle Splitting type |
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Line arrangements and configurations of points with an unexpected geometric property |
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2088@Funding text: [...]We also thank the Mathematisches Forschunginstitut Oberwolfach and the Banff International Research Station for supporting the workshops which gave us the opportunity to discuss and present our results.[...] |
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Line arrangements and configurations of points with an unexpected geometric property |
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Cook, David W. |
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Line arrangements and configurations of points with an unexpected geometric property |
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We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union X of fat points imposes on the complete linear system of curves in P-2 of fixed degree d, in terms of the occurrence of certain rational curves in the base locus of the linear subsystem defined by X. As a first step towards a new theory, we show that rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points. Moreover, motivated by work of Di Gennaro, Ilardi and Valles and of Faenzi and Valles, we relate our results to the failure of a strong Lefschetz property, and we give a Lefschetz-like criterion for Terao's conjecture on the freeness of line arrangements. Last seen: 02.11.2022 |
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We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union X of fat points imposes on the complete linear system of curves in P-2 of fixed degree d, in terms of the occurrence of certain rational curves in the base locus of the linear subsystem defined by X. As a first step towards a new theory, we show that rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points. Moreover, motivated by work of Di Gennaro, Ilardi and Valles and of Faenzi and Valles, we relate our results to the failure of a strong Lefschetz property, and we give a Lefschetz-like criterion for Terao's conjecture on the freeness of line arrangements. Last seen: 02.11.2022 |
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We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union X of fat points imposes on the complete linear system of curves in P-2 of fixed degree d, in terms of the occurrence of certain rational curves in the base locus of the linear subsystem defined by X. As a first step towards a new theory, we show that rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points. Moreover, motivated by work of Di Gennaro, Ilardi and Valles and of Faenzi and Valles, we relate our results to the failure of a strong Lefschetz property, and we give a Lefschetz-like criterion for Terao's conjecture on the freeness of line arrangements. Last seen: 02.11.2022 |
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code="f">--%%--</subfield><subfield code="d">--%%--</subfield><subfield code="e">--%%--</subfield><subfield code="j">--%%--</subfield><subfield code="k">Funding text: [...]We also thank the Mathematisches Forschunginstitut Oberwolfach and the Banff International Research Station for supporting the workshops which gave us the opportunity to discuss and present our results.[...]</subfield><subfield code="y">l01</subfield><subfield code="z">02-11-22</subfield></datafield><datafield tag="983" ind1=" " ind2=" "><subfield code="2">2088</subfield><subfield code="1">01</subfield><subfield code="x">DE-Frei3c</subfield><subfield code="8">00</subfield><subfield code="0">(DE-627)1294695886</subfield><subfield code="a">AMS:14</subfield><subfield code="b">Algebraic geometry</subfield></datafield><datafield tag="983" ind1=" " ind2=" "><subfield code="2">2088</subfield><subfield code="1">01</subfield><subfield code="x">DE-Frei3c</subfield><subfield code="8">00</subfield><subfield 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