Naïve blowups and canonical birationally commutative factors
Abstract In 2008, Rogalski and Zhang (Math Z 259(2):433–455, 2008) showed that if R is a strongly noetherian connected graded algebra over an algebraically closed field %${\Bbbk }%$, then R has a canonical birationally commutative factor. This factor is, up to finite dimension, a twisted homogeneous...
Ausführliche Beschreibung
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| Autor*in: |
Nevins, T. A. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Mathematische Zeitschrift - Berlin : Springer, 1918, 280(2015), 3-4 vom: 26. Mai, Seite 1125-1161 |
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| Übergeordnetes Werk: |
volume:280 ; year:2015 ; number:3-4 ; day:26 ; month:05 ; pages:1125-1161 |
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| DOI / URN: |
10.1007/s00209-015-1470-3 |
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SPR001927248 |
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| 100 | 1 | |a Nevins, T. A. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Naïve blowups and canonical birationally commutative factors |
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| 520 | |a Abstract In 2008, Rogalski and Zhang (Math Z 259(2):433–455, 2008) showed that if R is a strongly noetherian connected graded algebra over an algebraically closed field %${\Bbbk }%$, then R has a canonical birationally commutative factor. This factor is, up to finite dimension, a twisted homogeneous coordinate ring %$B(X, \mathcal {L}, \sigma )%$; here X is the projective parameter scheme for point modules over R, as well as tails of points in %${{\mathrm{Qgr-\!}}}R%$. (As usual, %$\sigma %$ is an automorphism of X, and %$\mathcal {L}%$ is a %$\sigma %$-ample invertible sheaf on X). We extend this result to a large class of noetherian (but not strongly noetherian) algebras. Specifically, let R be a noetherian connected graded %${\Bbbk }%$-algebra, where %${\Bbbk }%$ is an uncountable algebraically closed field. Let %$Y_\infty %$ denote the parameter space (or stack or proscheme) parameterizing R-point modules, and suppose there is a projective variety X that corepresents tails of points. There is a canonical map p:%$Y_\infty \rightarrow X%$. If the indeterminacy locus of %$p^{-1}%$ is 0-dimensional and X satisfies a mild technical assumption, we show that there is a homomorphism g:%$R \rightarrow B(X,\mathcal {L},\sigma )%$, and that g(R) is, up to finite dimension, a naive blowup on X in the sense of Keeler et al. (Duke Math J 126(3):491–546, 2005), Rogalski and Stafford (J Algebra 318(2):794–833, 2007) and satisfies a universal property. We further show that the point space %$Y_\infty %$ is noetherian. | ||
| 650 | 4 | |a Point space |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Noncommutative Hilbert scheme |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Canonical birationally commutative factor |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Naive blowup algebra |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Sierra, S. J. |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Mathematische Zeitschrift |d Berlin : Springer, 1918 |g 280(2015), 3-4 vom: 26. Mai, Seite 1125-1161 |w (DE-627)254630812 |w (DE-600)1462134-4 |x 1432-1823 |7 nnns |
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10.1007/s00209-015-1470-3 doi (DE-627)SPR001927248 (SPR)s00209-015-1470-3-e DE-627 ger DE-627 rakwb eng Nevins, T. A. verfasserin aut Naïve blowups and canonical birationally commutative factors 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract In 2008, Rogalski and Zhang (Math Z 259(2):433–455, 2008) showed that if R is a strongly noetherian connected graded algebra over an algebraically closed field %${\Bbbk }%$, then R has a canonical birationally commutative factor. This factor is, up to finite dimension, a twisted homogeneous coordinate ring %$B(X, \mathcal {L}, \sigma )%$; here X is the projective parameter scheme for point modules over R, as well as tails of points in %${{\mathrm{Qgr-\!}}}R%$. (As usual, %$\sigma %$ is an automorphism of X, and %$\mathcal {L}%$ is a %$\sigma %$-ample invertible sheaf on X). We extend this result to a large class of noetherian (but not strongly noetherian) algebras. Specifically, let R be a noetherian connected graded %${\Bbbk }%$-algebra, where %${\Bbbk }%$ is an uncountable algebraically closed field. Let %$Y_\infty %$ denote the parameter space (or stack or proscheme) parameterizing R-point modules, and suppose there is a projective variety X that corepresents tails of points. There is a canonical map p:%$Y_\infty \rightarrow X%$. If the indeterminacy locus of %$p^{-1}%$ is 0-dimensional and X satisfies a mild technical assumption, we show that there is a homomorphism g:%$R \rightarrow B(X,\mathcal {L},\sigma )%$, and that g(R) is, up to finite dimension, a naive blowup on X in the sense of Keeler et al. (Duke Math J 126(3):491–546, 2005), Rogalski and Stafford (J Algebra 318(2):794–833, 2007) and satisfies a universal property. We further show that the point space %$Y_\infty %$ is noetherian. Point space (dpeaa)DE-He213 Noncommutative Hilbert scheme (dpeaa)DE-He213 Canonical birationally commutative factor (dpeaa)DE-He213 Naive blowup algebra (dpeaa)DE-He213 Sierra, S. J. aut Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 280(2015), 3-4 vom: 26. Mai, Seite 1125-1161 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:280 year:2015 number:3-4 day:26 month:05 pages:1125-1161 https://dx.doi.org/10.1007/s00209-015-1470-3 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_2018 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_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 280 2015 3-4 26 05 1125-1161 |
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10.1007/s00209-015-1470-3 doi (DE-627)SPR001927248 (SPR)s00209-015-1470-3-e DE-627 ger DE-627 rakwb eng Nevins, T. A. verfasserin aut Naïve blowups and canonical birationally commutative factors 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract In 2008, Rogalski and Zhang (Math Z 259(2):433–455, 2008) showed that if R is a strongly noetherian connected graded algebra over an algebraically closed field %${\Bbbk }%$, then R has a canonical birationally commutative factor. This factor is, up to finite dimension, a twisted homogeneous coordinate ring %$B(X, \mathcal {L}, \sigma )%$; here X is the projective parameter scheme for point modules over R, as well as tails of points in %${{\mathrm{Qgr-\!}}}R%$. (As usual, %$\sigma %$ is an automorphism of X, and %$\mathcal {L}%$ is a %$\sigma %$-ample invertible sheaf on X). We extend this result to a large class of noetherian (but not strongly noetherian) algebras. Specifically, let R be a noetherian connected graded %${\Bbbk }%$-algebra, where %${\Bbbk }%$ is an uncountable algebraically closed field. Let %$Y_\infty %$ denote the parameter space (or stack or proscheme) parameterizing R-point modules, and suppose there is a projective variety X that corepresents tails of points. There is a canonical map p:%$Y_\infty \rightarrow X%$. If the indeterminacy locus of %$p^{-1}%$ is 0-dimensional and X satisfies a mild technical assumption, we show that there is a homomorphism g:%$R \rightarrow B(X,\mathcal {L},\sigma )%$, and that g(R) is, up to finite dimension, a naive blowup on X in the sense of Keeler et al. (Duke Math J 126(3):491–546, 2005), Rogalski and Stafford (J Algebra 318(2):794–833, 2007) and satisfies a universal property. We further show that the point space %$Y_\infty %$ is noetherian. Point space (dpeaa)DE-He213 Noncommutative Hilbert scheme (dpeaa)DE-He213 Canonical birationally commutative factor (dpeaa)DE-He213 Naive blowup algebra (dpeaa)DE-He213 Sierra, S. J. aut Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 280(2015), 3-4 vom: 26. Mai, Seite 1125-1161 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:280 year:2015 number:3-4 day:26 month:05 pages:1125-1161 https://dx.doi.org/10.1007/s00209-015-1470-3 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_2018 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_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 280 2015 3-4 26 05 1125-1161 |
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10.1007/s00209-015-1470-3 doi (DE-627)SPR001927248 (SPR)s00209-015-1470-3-e DE-627 ger DE-627 rakwb eng Nevins, T. A. verfasserin aut Naïve blowups and canonical birationally commutative factors 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract In 2008, Rogalski and Zhang (Math Z 259(2):433–455, 2008) showed that if R is a strongly noetherian connected graded algebra over an algebraically closed field %${\Bbbk }%$, then R has a canonical birationally commutative factor. This factor is, up to finite dimension, a twisted homogeneous coordinate ring %$B(X, \mathcal {L}, \sigma )%$; here X is the projective parameter scheme for point modules over R, as well as tails of points in %${{\mathrm{Qgr-\!}}}R%$. (As usual, %$\sigma %$ is an automorphism of X, and %$\mathcal {L}%$ is a %$\sigma %$-ample invertible sheaf on X). We extend this result to a large class of noetherian (but not strongly noetherian) algebras. Specifically, let R be a noetherian connected graded %${\Bbbk }%$-algebra, where %${\Bbbk }%$ is an uncountable algebraically closed field. Let %$Y_\infty %$ denote the parameter space (or stack or proscheme) parameterizing R-point modules, and suppose there is a projective variety X that corepresents tails of points. There is a canonical map p:%$Y_\infty \rightarrow X%$. If the indeterminacy locus of %$p^{-1}%$ is 0-dimensional and X satisfies a mild technical assumption, we show that there is a homomorphism g:%$R \rightarrow B(X,\mathcal {L},\sigma )%$, and that g(R) is, up to finite dimension, a naive blowup on X in the sense of Keeler et al. (Duke Math J 126(3):491–546, 2005), Rogalski and Stafford (J Algebra 318(2):794–833, 2007) and satisfies a universal property. We further show that the point space %$Y_\infty %$ is noetherian. Point space (dpeaa)DE-He213 Noncommutative Hilbert scheme (dpeaa)DE-He213 Canonical birationally commutative factor (dpeaa)DE-He213 Naive blowup algebra (dpeaa)DE-He213 Sierra, S. J. aut Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 280(2015), 3-4 vom: 26. Mai, Seite 1125-1161 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:280 year:2015 number:3-4 day:26 month:05 pages:1125-1161 https://dx.doi.org/10.1007/s00209-015-1470-3 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_2018 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_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 280 2015 3-4 26 05 1125-1161 |
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10.1007/s00209-015-1470-3 doi (DE-627)SPR001927248 (SPR)s00209-015-1470-3-e DE-627 ger DE-627 rakwb eng Nevins, T. A. verfasserin aut Naïve blowups and canonical birationally commutative factors 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract In 2008, Rogalski and Zhang (Math Z 259(2):433–455, 2008) showed that if R is a strongly noetherian connected graded algebra over an algebraically closed field %${\Bbbk }%$, then R has a canonical birationally commutative factor. This factor is, up to finite dimension, a twisted homogeneous coordinate ring %$B(X, \mathcal {L}, \sigma )%$; here X is the projective parameter scheme for point modules over R, as well as tails of points in %${{\mathrm{Qgr-\!}}}R%$. (As usual, %$\sigma %$ is an automorphism of X, and %$\mathcal {L}%$ is a %$\sigma %$-ample invertible sheaf on X). We extend this result to a large class of noetherian (but not strongly noetherian) algebras. Specifically, let R be a noetherian connected graded %${\Bbbk }%$-algebra, where %${\Bbbk }%$ is an uncountable algebraically closed field. Let %$Y_\infty %$ denote the parameter space (or stack or proscheme) parameterizing R-point modules, and suppose there is a projective variety X that corepresents tails of points. There is a canonical map p:%$Y_\infty \rightarrow X%$. If the indeterminacy locus of %$p^{-1}%$ is 0-dimensional and X satisfies a mild technical assumption, we show that there is a homomorphism g:%$R \rightarrow B(X,\mathcal {L},\sigma )%$, and that g(R) is, up to finite dimension, a naive blowup on X in the sense of Keeler et al. (Duke Math J 126(3):491–546, 2005), Rogalski and Stafford (J Algebra 318(2):794–833, 2007) and satisfies a universal property. We further show that the point space %$Y_\infty %$ is noetherian. Point space (dpeaa)DE-He213 Noncommutative Hilbert scheme (dpeaa)DE-He213 Canonical birationally commutative factor (dpeaa)DE-He213 Naive blowup algebra (dpeaa)DE-He213 Sierra, S. J. aut Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 280(2015), 3-4 vom: 26. Mai, Seite 1125-1161 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:280 year:2015 number:3-4 day:26 month:05 pages:1125-1161 https://dx.doi.org/10.1007/s00209-015-1470-3 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_2018 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_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 280 2015 3-4 26 05 1125-1161 |
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10.1007/s00209-015-1470-3 doi (DE-627)SPR001927248 (SPR)s00209-015-1470-3-e DE-627 ger DE-627 rakwb eng Nevins, T. A. verfasserin aut Naïve blowups and canonical birationally commutative factors 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract In 2008, Rogalski and Zhang (Math Z 259(2):433–455, 2008) showed that if R is a strongly noetherian connected graded algebra over an algebraically closed field %${\Bbbk }%$, then R has a canonical birationally commutative factor. This factor is, up to finite dimension, a twisted homogeneous coordinate ring %$B(X, \mathcal {L}, \sigma )%$; here X is the projective parameter scheme for point modules over R, as well as tails of points in %${{\mathrm{Qgr-\!}}}R%$. (As usual, %$\sigma %$ is an automorphism of X, and %$\mathcal {L}%$ is a %$\sigma %$-ample invertible sheaf on X). We extend this result to a large class of noetherian (but not strongly noetherian) algebras. Specifically, let R be a noetherian connected graded %${\Bbbk }%$-algebra, where %${\Bbbk }%$ is an uncountable algebraically closed field. Let %$Y_\infty %$ denote the parameter space (or stack or proscheme) parameterizing R-point modules, and suppose there is a projective variety X that corepresents tails of points. There is a canonical map p:%$Y_\infty \rightarrow X%$. If the indeterminacy locus of %$p^{-1}%$ is 0-dimensional and X satisfies a mild technical assumption, we show that there is a homomorphism g:%$R \rightarrow B(X,\mathcal {L},\sigma )%$, and that g(R) is, up to finite dimension, a naive blowup on X in the sense of Keeler et al. (Duke Math J 126(3):491–546, 2005), Rogalski and Stafford (J Algebra 318(2):794–833, 2007) and satisfies a universal property. We further show that the point space %$Y_\infty %$ is noetherian. Point space (dpeaa)DE-He213 Noncommutative Hilbert scheme (dpeaa)DE-He213 Canonical birationally commutative factor (dpeaa)DE-He213 Naive blowup algebra (dpeaa)DE-He213 Sierra, S. J. aut Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 280(2015), 3-4 vom: 26. Mai, Seite 1125-1161 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:280 year:2015 number:3-4 day:26 month:05 pages:1125-1161 https://dx.doi.org/10.1007/s00209-015-1470-3 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_2018 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_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 280 2015 3-4 26 05 1125-1161 |
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Enthalten in Mathematische Zeitschrift 280(2015), 3-4 vom: 26. Mai, Seite 1125-1161 volume:280 year:2015 number:3-4 day:26 month:05 pages:1125-1161 |
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Enthalten in Mathematische Zeitschrift 280(2015), 3-4 vom: 26. Mai, Seite 1125-1161 volume:280 year:2015 number:3-4 day:26 month:05 pages:1125-1161 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR001927248</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327145323.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2015 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00209-015-1470-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR001927248</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00209-015-1470-3-e</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">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Nevins, T. A.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Naïve blowups and canonical birationally commutative factors</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015</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">© Springer-Verlag Berlin Heidelberg 2015</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In 2008, Rogalski and Zhang (Math Z 259(2):433–455, 2008) showed that if R is a strongly noetherian connected graded algebra over an algebraically closed field %${\Bbbk }%$, then R has a canonical birationally commutative factor. This factor is, up to finite dimension, a twisted homogeneous coordinate ring %$B(X, \mathcal {L}, \sigma )%$; here X is the projective parameter scheme for point modules over R, as well as tails of points in %${{\mathrm{Qgr-\!}}}R%$. (As usual, %$\sigma %$ is an automorphism of X, and %$\mathcal {L}%$ is a %$\sigma %$-ample invertible sheaf on X). We extend this result to a large class of noetherian (but not strongly noetherian) algebras. Specifically, let R be a noetherian connected graded %${\Bbbk }%$-algebra, where %${\Bbbk }%$ is an uncountable algebraically closed field. Let %$Y_\infty %$ denote the parameter space (or stack or proscheme) parameterizing R-point modules, and suppose there is a projective variety X that corepresents tails of points. There is a canonical map p:%$Y_\infty \rightarrow X%$. If the indeterminacy locus of %$p^{-1}%$ is 0-dimensional and X satisfies a mild technical assumption, we show that there is a homomorphism g:%$R \rightarrow B(X,\mathcal {L},\sigma )%$, and that g(R) is, up to finite dimension, a naive blowup on X in the sense of Keeler et al. (Duke Math J 126(3):491–546, 2005), Rogalski and Stafford (J Algebra 318(2):794–833, 2007) and satisfies a universal property. We further show that the point space %$Y_\infty %$ is noetherian.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Point space</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Noncommutative Hilbert scheme</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Canonical birationally commutative factor</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Naive blowup algebra</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sierra, S. 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Nevins, T. A. |
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Nevins, T. A. misc Point space misc Noncommutative Hilbert scheme misc Canonical birationally commutative factor misc Naive blowup algebra Naïve blowups and canonical birationally commutative factors |
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Naïve blowups and canonical birationally commutative factors Point space (dpeaa)DE-He213 Noncommutative Hilbert scheme (dpeaa)DE-He213 Canonical birationally commutative factor (dpeaa)DE-He213 Naive blowup algebra (dpeaa)DE-He213 |
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naïve blowups and canonical birationally commutative factors |
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Naïve blowups and canonical birationally commutative factors |
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Abstract In 2008, Rogalski and Zhang (Math Z 259(2):433–455, 2008) showed that if R is a strongly noetherian connected graded algebra over an algebraically closed field %${\Bbbk }%$, then R has a canonical birationally commutative factor. This factor is, up to finite dimension, a twisted homogeneous coordinate ring %$B(X, \mathcal {L}, \sigma )%$; here X is the projective parameter scheme for point modules over R, as well as tails of points in %${{\mathrm{Qgr-\!}}}R%$. (As usual, %$\sigma %$ is an automorphism of X, and %$\mathcal {L}%$ is a %$\sigma %$-ample invertible sheaf on X). We extend this result to a large class of noetherian (but not strongly noetherian) algebras. Specifically, let R be a noetherian connected graded %${\Bbbk }%$-algebra, where %${\Bbbk }%$ is an uncountable algebraically closed field. Let %$Y_\infty %$ denote the parameter space (or stack or proscheme) parameterizing R-point modules, and suppose there is a projective variety X that corepresents tails of points. There is a canonical map p:%$Y_\infty \rightarrow X%$. If the indeterminacy locus of %$p^{-1}%$ is 0-dimensional and X satisfies a mild technical assumption, we show that there is a homomorphism g:%$R \rightarrow B(X,\mathcal {L},\sigma )%$, and that g(R) is, up to finite dimension, a naive blowup on X in the sense of Keeler et al. (Duke Math J 126(3):491–546, 2005), Rogalski and Stafford (J Algebra 318(2):794–833, 2007) and satisfies a universal property. We further show that the point space %$Y_\infty %$ is noetherian. © Springer-Verlag Berlin Heidelberg 2015 |
| abstractGer |
Abstract In 2008, Rogalski and Zhang (Math Z 259(2):433–455, 2008) showed that if R is a strongly noetherian connected graded algebra over an algebraically closed field %${\Bbbk }%$, then R has a canonical birationally commutative factor. This factor is, up to finite dimension, a twisted homogeneous coordinate ring %$B(X, \mathcal {L}, \sigma )%$; here X is the projective parameter scheme for point modules over R, as well as tails of points in %${{\mathrm{Qgr-\!}}}R%$. (As usual, %$\sigma %$ is an automorphism of X, and %$\mathcal {L}%$ is a %$\sigma %$-ample invertible sheaf on X). We extend this result to a large class of noetherian (but not strongly noetherian) algebras. Specifically, let R be a noetherian connected graded %${\Bbbk }%$-algebra, where %${\Bbbk }%$ is an uncountable algebraically closed field. Let %$Y_\infty %$ denote the parameter space (or stack or proscheme) parameterizing R-point modules, and suppose there is a projective variety X that corepresents tails of points. There is a canonical map p:%$Y_\infty \rightarrow X%$. If the indeterminacy locus of %$p^{-1}%$ is 0-dimensional and X satisfies a mild technical assumption, we show that there is a homomorphism g:%$R \rightarrow B(X,\mathcal {L},\sigma )%$, and that g(R) is, up to finite dimension, a naive blowup on X in the sense of Keeler et al. (Duke Math J 126(3):491–546, 2005), Rogalski and Stafford (J Algebra 318(2):794–833, 2007) and satisfies a universal property. We further show that the point space %$Y_\infty %$ is noetherian. © Springer-Verlag Berlin Heidelberg 2015 |
| abstract_unstemmed |
Abstract In 2008, Rogalski and Zhang (Math Z 259(2):433–455, 2008) showed that if R is a strongly noetherian connected graded algebra over an algebraically closed field %${\Bbbk }%$, then R has a canonical birationally commutative factor. This factor is, up to finite dimension, a twisted homogeneous coordinate ring %$B(X, \mathcal {L}, \sigma )%$; here X is the projective parameter scheme for point modules over R, as well as tails of points in %${{\mathrm{Qgr-\!}}}R%$. (As usual, %$\sigma %$ is an automorphism of X, and %$\mathcal {L}%$ is a %$\sigma %$-ample invertible sheaf on X). We extend this result to a large class of noetherian (but not strongly noetherian) algebras. Specifically, let R be a noetherian connected graded %${\Bbbk }%$-algebra, where %${\Bbbk }%$ is an uncountable algebraically closed field. Let %$Y_\infty %$ denote the parameter space (or stack or proscheme) parameterizing R-point modules, and suppose there is a projective variety X that corepresents tails of points. There is a canonical map p:%$Y_\infty \rightarrow X%$. If the indeterminacy locus of %$p^{-1}%$ is 0-dimensional and X satisfies a mild technical assumption, we show that there is a homomorphism g:%$R \rightarrow B(X,\mathcal {L},\sigma )%$, and that g(R) is, up to finite dimension, a naive blowup on X in the sense of Keeler et al. (Duke Math J 126(3):491–546, 2005), Rogalski and Stafford (J Algebra 318(2):794–833, 2007) and satisfies a universal property. We further show that the point space %$Y_\infty %$ is noetherian. © Springer-Verlag Berlin Heidelberg 2015 |
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Naïve blowups and canonical birationally commutative factors |
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Sierra, S. J. |
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| score |
7.398053 |