Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g
Abstract We denote by %$\mathcal {H}_{d,g,r}%$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in %$\mathbb {P}^r%$. In this note, we show that any non-empty %$\mathcal {H}_...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Keem, Changho [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer International Publishing AG 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Archiv der Mathematik - Berlin : Springer, 1948, 109(2017), 6 vom: 16. Aug., Seite 521-527 |
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| Übergeordnetes Werk: |
volume:109 ; year:2017 ; number:6 ; day:16 ; month:08 ; pages:521-527 |
| Links: |
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| DOI / URN: |
10.1007/s00013-017-1083-7 |
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| Katalog-ID: |
SPR000061182 |
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| 100 | 1 | |a Keem, Changho |e verfasserin |0 (orcid)0000-0002-4948-2966 |4 aut | |
| 245 | 1 | 0 | |a Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g |
| 264 | 1 | |c 2017 | |
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| 520 | |a Abstract We denote by %$\mathcal {H}_{d,g,r}%$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in %$\mathbb {P}^r%$. In this note, we show that any non-empty %$\mathcal {H}_{g+2,g,4}%$ is irreducible, generically smooth, and has the expected dimension %$4g+11%$ without any restriction on the genus g. Our result augments the irreducibility result obtained earlier by Iliev (Proc Am Math Soc 134:2823–2832, 2006), in which several low genus %$g\le 10%$ cases have been left untreated. | ||
| 650 | 4 | |a Hilbert scheme |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Algebraic curves |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Linear series |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Kim, Yun-Hwan |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Archiv der Mathematik |d Berlin : Springer, 1948 |g 109(2017), 6 vom: 16. Aug., Seite 521-527 |w (DE-627)253389976 |w (DE-600)1458441-4 |x 1420-8938 |7 nnns |
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10.1007/s00013-017-1083-7 doi (DE-627)SPR000061182 (SPR)s00013-017-1083-7-e DE-627 ger DE-627 rakwb eng Keem, Changho verfasserin (orcid)0000-0002-4948-2966 aut Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing AG 2017 Abstract We denote by %$\mathcal {H}_{d,g,r}%$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in %$\mathbb {P}^r%$. In this note, we show that any non-empty %$\mathcal {H}_{g+2,g,4}%$ is irreducible, generically smooth, and has the expected dimension %$4g+11%$ without any restriction on the genus g. Our result augments the irreducibility result obtained earlier by Iliev (Proc Am Math Soc 134:2823–2832, 2006), in which several low genus %$g\le 10%$ cases have been left untreated. Hilbert scheme (dpeaa)DE-He213 Algebraic curves (dpeaa)DE-He213 Linear series (dpeaa)DE-He213 Kim, Yun-Hwan aut Enthalten in Archiv der Mathematik Berlin : Springer, 1948 109(2017), 6 vom: 16. Aug., Seite 521-527 (DE-627)253389976 (DE-600)1458441-4 1420-8938 nnns volume:109 year:2017 number:6 day:16 month:08 pages:521-527 https://dx.doi.org/10.1007/s00013-017-1083-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 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_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 109 2017 6 16 08 521-527 |
| spelling |
10.1007/s00013-017-1083-7 doi (DE-627)SPR000061182 (SPR)s00013-017-1083-7-e DE-627 ger DE-627 rakwb eng Keem, Changho verfasserin (orcid)0000-0002-4948-2966 aut Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing AG 2017 Abstract We denote by %$\mathcal {H}_{d,g,r}%$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in %$\mathbb {P}^r%$. In this note, we show that any non-empty %$\mathcal {H}_{g+2,g,4}%$ is irreducible, generically smooth, and has the expected dimension %$4g+11%$ without any restriction on the genus g. Our result augments the irreducibility result obtained earlier by Iliev (Proc Am Math Soc 134:2823–2832, 2006), in which several low genus %$g\le 10%$ cases have been left untreated. Hilbert scheme (dpeaa)DE-He213 Algebraic curves (dpeaa)DE-He213 Linear series (dpeaa)DE-He213 Kim, Yun-Hwan aut Enthalten in Archiv der Mathematik Berlin : Springer, 1948 109(2017), 6 vom: 16. Aug., Seite 521-527 (DE-627)253389976 (DE-600)1458441-4 1420-8938 nnns volume:109 year:2017 number:6 day:16 month:08 pages:521-527 https://dx.doi.org/10.1007/s00013-017-1083-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 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_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 109 2017 6 16 08 521-527 |
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10.1007/s00013-017-1083-7 doi (DE-627)SPR000061182 (SPR)s00013-017-1083-7-e DE-627 ger DE-627 rakwb eng Keem, Changho verfasserin (orcid)0000-0002-4948-2966 aut Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing AG 2017 Abstract We denote by %$\mathcal {H}_{d,g,r}%$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in %$\mathbb {P}^r%$. In this note, we show that any non-empty %$\mathcal {H}_{g+2,g,4}%$ is irreducible, generically smooth, and has the expected dimension %$4g+11%$ without any restriction on the genus g. Our result augments the irreducibility result obtained earlier by Iliev (Proc Am Math Soc 134:2823–2832, 2006), in which several low genus %$g\le 10%$ cases have been left untreated. Hilbert scheme (dpeaa)DE-He213 Algebraic curves (dpeaa)DE-He213 Linear series (dpeaa)DE-He213 Kim, Yun-Hwan aut Enthalten in Archiv der Mathematik Berlin : Springer, 1948 109(2017), 6 vom: 16. Aug., Seite 521-527 (DE-627)253389976 (DE-600)1458441-4 1420-8938 nnns volume:109 year:2017 number:6 day:16 month:08 pages:521-527 https://dx.doi.org/10.1007/s00013-017-1083-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 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_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 109 2017 6 16 08 521-527 |
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10.1007/s00013-017-1083-7 doi (DE-627)SPR000061182 (SPR)s00013-017-1083-7-e DE-627 ger DE-627 rakwb eng Keem, Changho verfasserin (orcid)0000-0002-4948-2966 aut Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing AG 2017 Abstract We denote by %$\mathcal {H}_{d,g,r}%$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in %$\mathbb {P}^r%$. In this note, we show that any non-empty %$\mathcal {H}_{g+2,g,4}%$ is irreducible, generically smooth, and has the expected dimension %$4g+11%$ without any restriction on the genus g. Our result augments the irreducibility result obtained earlier by Iliev (Proc Am Math Soc 134:2823–2832, 2006), in which several low genus %$g\le 10%$ cases have been left untreated. Hilbert scheme (dpeaa)DE-He213 Algebraic curves (dpeaa)DE-He213 Linear series (dpeaa)DE-He213 Kim, Yun-Hwan aut Enthalten in Archiv der Mathematik Berlin : Springer, 1948 109(2017), 6 vom: 16. Aug., Seite 521-527 (DE-627)253389976 (DE-600)1458441-4 1420-8938 nnns volume:109 year:2017 number:6 day:16 month:08 pages:521-527 https://dx.doi.org/10.1007/s00013-017-1083-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 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_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 109 2017 6 16 08 521-527 |
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10.1007/s00013-017-1083-7 doi (DE-627)SPR000061182 (SPR)s00013-017-1083-7-e DE-627 ger DE-627 rakwb eng Keem, Changho verfasserin (orcid)0000-0002-4948-2966 aut Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing AG 2017 Abstract We denote by %$\mathcal {H}_{d,g,r}%$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in %$\mathbb {P}^r%$. In this note, we show that any non-empty %$\mathcal {H}_{g+2,g,4}%$ is irreducible, generically smooth, and has the expected dimension %$4g+11%$ without any restriction on the genus g. Our result augments the irreducibility result obtained earlier by Iliev (Proc Am Math Soc 134:2823–2832, 2006), in which several low genus %$g\le 10%$ cases have been left untreated. Hilbert scheme (dpeaa)DE-He213 Algebraic curves (dpeaa)DE-He213 Linear series (dpeaa)DE-He213 Kim, Yun-Hwan aut Enthalten in Archiv der Mathematik Berlin : Springer, 1948 109(2017), 6 vom: 16. Aug., Seite 521-527 (DE-627)253389976 (DE-600)1458441-4 1420-8938 nnns volume:109 year:2017 number:6 day:16 month:08 pages:521-527 https://dx.doi.org/10.1007/s00013-017-1083-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 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_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 109 2017 6 16 08 521-527 |
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Keem, Changho |
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Keem, Changho misc Hilbert scheme misc Algebraic curves misc Linear series Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g |
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Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g Hilbert scheme (dpeaa)DE-He213 Algebraic curves (dpeaa)DE-He213 Linear series (dpeaa)DE-He213 |
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Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g |
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Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g |
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irreducibility of the hilbert scheme of smooth curves in %$\mathbb {p}^4%$ of degree %$g+2%$ and genus g |
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Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g |
| abstract |
Abstract We denote by %$\mathcal {H}_{d,g,r}%$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in %$\mathbb {P}^r%$. In this note, we show that any non-empty %$\mathcal {H}_{g+2,g,4}%$ is irreducible, generically smooth, and has the expected dimension %$4g+11%$ without any restriction on the genus g. Our result augments the irreducibility result obtained earlier by Iliev (Proc Am Math Soc 134:2823–2832, 2006), in which several low genus %$g\le 10%$ cases have been left untreated. © Springer International Publishing AG 2017 |
| abstractGer |
Abstract We denote by %$\mathcal {H}_{d,g,r}%$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in %$\mathbb {P}^r%$. In this note, we show that any non-empty %$\mathcal {H}_{g+2,g,4}%$ is irreducible, generically smooth, and has the expected dimension %$4g+11%$ without any restriction on the genus g. Our result augments the irreducibility result obtained earlier by Iliev (Proc Am Math Soc 134:2823–2832, 2006), in which several low genus %$g\le 10%$ cases have been left untreated. © Springer International Publishing AG 2017 |
| abstract_unstemmed |
Abstract We denote by %$\mathcal {H}_{d,g,r}%$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in %$\mathbb {P}^r%$. In this note, we show that any non-empty %$\mathcal {H}_{g+2,g,4}%$ is irreducible, generically smooth, and has the expected dimension %$4g+11%$ without any restriction on the genus g. Our result augments the irreducibility result obtained earlier by Iliev (Proc Am Math Soc 134:2823–2832, 2006), in which several low genus %$g\le 10%$ cases have been left untreated. © Springer International Publishing AG 2017 |
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Irreducibility of the Hilbert scheme of smooth curves in %$\mathbb {P}^4%$ of degree %$g+2%$ and genus g |
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https://dx.doi.org/10.1007/s00013-017-1083-7 |
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Kim, Yun-Hwan |
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10.1007/s00013-017-1083-7 |
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2024-07-03T13:46:17.864Z |
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