Algebraic Hamiltonian actions

Abstract In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X. We study the quotient morphism %${\mu_{G,X}//G : X//G \rightarrow \mathfrak{g} //G}%$ of the moment map %${\mu_{G,X} : X\rightarrow \mathfrak{g}}%$ . We prove...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Losev, Ivan V. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2009

Schlagwörter:	Poisson variety Reductive group Hamiltonian action Moment map

Anmerkung:	© Springer-Verlag 2009

Übergeordnetes Werk:	Enthalten in: Mathematische Zeitschrift - Berlin : Springer, 1918, 263(2009), 3 vom: 14. Aug., Seite 685-723
Übergeordnetes Werk:	volume:263 ; year:2009 ; number:3 ; day:14 ; month:08 ; pages:685-723

Links:	Volltext

DOI / URN:	10.1007/s00209-009-0587-7

Katalog-ID:	SPR001916076

Internformat


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520			\|a Abstract In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X. We study the quotient morphism %${\mu_{G,X}//G : X//G \rightarrow \mathfrak{g} //G}%$ of the moment map %${\mu_{G,X} : X\rightarrow \mathfrak{g}}%$ . We prove that for a wide class of Hamiltonian actions (including, for example, actions on generically symplectic varieties) all fibers of the morphism μG,X//G have the same dimension. We also study the “Stein factorization” of μG,X//G. Namely, let CG,X denote the spectrum of the integral closure of %${\mu_{G,X}^{*}(\mathbb{K}[\mathfrak{g}]^G)}%$ in %${\mathbb{K}(X)^G}%$ . We investigate the structure of the %${\mathfrak{g} //G}%$ -scheme CG,X. Our results partially generalize those obtained by F. Knop for the actions on cotangent bundles and symplectic vector spaces.
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650		4	\|a Hamiltonian action \|7 (dpeaa)DE-He213
650		4	\|a Moment map \|7 (dpeaa)DE-He213
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912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_267
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2018
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
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matchkey_str	article:14321823:2009----::lerihmloi
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publishDate	2009
allfields	10.1007/s00209-009-0587-7 doi (DE-627)SPR001916076 (SPR)s00209-009-0587-7-e DE-627 ger DE-627 rakwb eng Losev, Ivan V. verfasserin aut Algebraic Hamiltonian actions 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2009 Abstract In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X. We study the quotient morphism %${\mu_{G,X}//G : X//G \rightarrow \mathfrak{g} //G}%$ of the moment map %${\mu_{G,X} : X\rightarrow \mathfrak{g}}%$ . We prove that for a wide class of Hamiltonian actions (including, for example, actions on generically symplectic varieties) all fibers of the morphism μG,X//G have the same dimension. We also study the “Stein factorization” of μG,X//G. Namely, let CG,X denote the spectrum of the integral closure of %${\mu_{G,X}^{*}(\mathbb{K}[\mathfrak{g}]^G)}%$ in %${\mathbb{K}(X)^G}%$ . We investigate the structure of the %${\mathfrak{g} //G}%$ -scheme CG,X. Our results partially generalize those obtained by F. Knop for the actions on cotangent bundles and symplectic vector spaces. Poisson variety (dpeaa)DE-He213 Reductive group (dpeaa)DE-He213 Hamiltonian action (dpeaa)DE-He213 Moment map (dpeaa)DE-He213 Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 263(2009), 3 vom: 14. Aug., Seite 685-723 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:263 year:2009 number:3 day:14 month:08 pages:685-723 https://dx.doi.org/10.1007/s00209-009-0587-7 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_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 263 2009 3 14 08 685-723
spelling	10.1007/s00209-009-0587-7 doi (DE-627)SPR001916076 (SPR)s00209-009-0587-7-e DE-627 ger DE-627 rakwb eng Losev, Ivan V. verfasserin aut Algebraic Hamiltonian actions 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2009 Abstract In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X. We study the quotient morphism %${\mu_{G,X}//G : X//G \rightarrow \mathfrak{g} //G}%$ of the moment map %${\mu_{G,X} : X\rightarrow \mathfrak{g}}%$ . We prove that for a wide class of Hamiltonian actions (including, for example, actions on generically symplectic varieties) all fibers of the morphism μG,X//G have the same dimension. We also study the “Stein factorization” of μG,X//G. Namely, let CG,X denote the spectrum of the integral closure of %${\mu_{G,X}^{*}(\mathbb{K}[\mathfrak{g}]^G)}%$ in %${\mathbb{K}(X)^G}%$ . We investigate the structure of the %${\mathfrak{g} //G}%$ -scheme CG,X. Our results partially generalize those obtained by F. Knop for the actions on cotangent bundles and symplectic vector spaces. Poisson variety (dpeaa)DE-He213 Reductive group (dpeaa)DE-He213 Hamiltonian action (dpeaa)DE-He213 Moment map (dpeaa)DE-He213 Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 263(2009), 3 vom: 14. Aug., Seite 685-723 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:263 year:2009 number:3 day:14 month:08 pages:685-723 https://dx.doi.org/10.1007/s00209-009-0587-7 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_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 263 2009 3 14 08 685-723
allfields_unstemmed	10.1007/s00209-009-0587-7 doi (DE-627)SPR001916076 (SPR)s00209-009-0587-7-e DE-627 ger DE-627 rakwb eng Losev, Ivan V. verfasserin aut Algebraic Hamiltonian actions 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2009 Abstract In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X. We study the quotient morphism %${\mu_{G,X}//G : X//G \rightarrow \mathfrak{g} //G}%$ of the moment map %${\mu_{G,X} : X\rightarrow \mathfrak{g}}%$ . We prove that for a wide class of Hamiltonian actions (including, for example, actions on generically symplectic varieties) all fibers of the morphism μG,X//G have the same dimension. We also study the “Stein factorization” of μG,X//G. Namely, let CG,X denote the spectrum of the integral closure of %${\mu_{G,X}^{*}(\mathbb{K}[\mathfrak{g}]^G)}%$ in %${\mathbb{K}(X)^G}%$ . We investigate the structure of the %${\mathfrak{g} //G}%$ -scheme CG,X. Our results partially generalize those obtained by F. Knop for the actions on cotangent bundles and symplectic vector spaces. Poisson variety (dpeaa)DE-He213 Reductive group (dpeaa)DE-He213 Hamiltonian action (dpeaa)DE-He213 Moment map (dpeaa)DE-He213 Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 263(2009), 3 vom: 14. Aug., Seite 685-723 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:263 year:2009 number:3 day:14 month:08 pages:685-723 https://dx.doi.org/10.1007/s00209-009-0587-7 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_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 263 2009 3 14 08 685-723
allfieldsGer	10.1007/s00209-009-0587-7 doi (DE-627)SPR001916076 (SPR)s00209-009-0587-7-e DE-627 ger DE-627 rakwb eng Losev, Ivan V. verfasserin aut Algebraic Hamiltonian actions 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2009 Abstract In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X. We study the quotient morphism %${\mu_{G,X}//G : X//G \rightarrow \mathfrak{g} //G}%$ of the moment map %${\mu_{G,X} : X\rightarrow \mathfrak{g}}%$ . We prove that for a wide class of Hamiltonian actions (including, for example, actions on generically symplectic varieties) all fibers of the morphism μG,X//G have the same dimension. We also study the “Stein factorization” of μG,X//G. Namely, let CG,X denote the spectrum of the integral closure of %${\mu_{G,X}^{*}(\mathbb{K}[\mathfrak{g}]^G)}%$ in %${\mathbb{K}(X)^G}%$ . We investigate the structure of the %${\mathfrak{g} //G}%$ -scheme CG,X. Our results partially generalize those obtained by F. Knop for the actions on cotangent bundles and symplectic vector spaces. Poisson variety (dpeaa)DE-He213 Reductive group (dpeaa)DE-He213 Hamiltonian action (dpeaa)DE-He213 Moment map (dpeaa)DE-He213 Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 263(2009), 3 vom: 14. Aug., Seite 685-723 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:263 year:2009 number:3 day:14 month:08 pages:685-723 https://dx.doi.org/10.1007/s00209-009-0587-7 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_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 263 2009 3 14 08 685-723
allfieldsSound	10.1007/s00209-009-0587-7 doi (DE-627)SPR001916076 (SPR)s00209-009-0587-7-e DE-627 ger DE-627 rakwb eng Losev, Ivan V. verfasserin aut Algebraic Hamiltonian actions 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2009 Abstract In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X. We study the quotient morphism %${\mu_{G,X}//G : X//G \rightarrow \mathfrak{g} //G}%$ of the moment map %${\mu_{G,X} : X\rightarrow \mathfrak{g}}%$ . We prove that for a wide class of Hamiltonian actions (including, for example, actions on generically symplectic varieties) all fibers of the morphism μG,X//G have the same dimension. We also study the “Stein factorization” of μG,X//G. Namely, let CG,X denote the spectrum of the integral closure of %${\mu_{G,X}^{*}(\mathbb{K}[\mathfrak{g}]^G)}%$ in %${\mathbb{K}(X)^G}%$ . We investigate the structure of the %${\mathfrak{g} //G}%$ -scheme CG,X. Our results partially generalize those obtained by F. Knop for the actions on cotangent bundles and symplectic vector spaces. Poisson variety (dpeaa)DE-He213 Reductive group (dpeaa)DE-He213 Hamiltonian action (dpeaa)DE-He213 Moment map (dpeaa)DE-He213 Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 263(2009), 3 vom: 14. Aug., Seite 685-723 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:263 year:2009 number:3 day:14 month:08 pages:685-723 https://dx.doi.org/10.1007/s00209-009-0587-7 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_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 263 2009 3 14 08 685-723
language	English
source	Enthalten in Mathematische Zeitschrift 263(2009), 3 vom: 14. Aug., Seite 685-723 volume:263 year:2009 number:3 day:14 month:08 pages:685-723
sourceStr	Enthalten in Mathematische Zeitschrift 263(2009), 3 vom: 14. Aug., Seite 685-723 volume:263 year:2009 number:3 day:14 month:08 pages:685-723
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Poisson variety Reductive group Hamiltonian action Moment map
isfreeaccess_bool	false
container_title	Mathematische Zeitschrift
authorswithroles_txt_mv	Losev, Ivan V. @@aut@@
publishDateDaySort_date	2009-08-14T00:00:00Z
hierarchy_top_id	254630812
id	SPR001916076
language_de	englisch
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author	Losev, Ivan V.
spellingShingle	Losev, Ivan V. misc Poisson variety misc Reductive group misc Hamiltonian action misc Moment map Algebraic Hamiltonian actions
authorStr	Losev, Ivan V.
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topic_title	Algebraic Hamiltonian actions Poisson variety (dpeaa)DE-He213 Reductive group (dpeaa)DE-He213 Hamiltonian action (dpeaa)DE-He213 Moment map (dpeaa)DE-He213
topic	misc Poisson variety misc Reductive group misc Hamiltonian action misc Moment map
topic_unstemmed	misc Poisson variety misc Reductive group misc Hamiltonian action misc Moment map
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title	Algebraic Hamiltonian actions
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title_full	Algebraic Hamiltonian actions
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title_sort	algebraic hamiltonian actions
title_auth	Algebraic Hamiltonian actions
abstract	Abstract In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X. We study the quotient morphism %${\mu_{G,X}//G : X//G \rightarrow \mathfrak{g} //G}%$ of the moment map %${\mu_{G,X} : X\rightarrow \mathfrak{g}}%$ . We prove that for a wide class of Hamiltonian actions (including, for example, actions on generically symplectic varieties) all fibers of the morphism μG,X//G have the same dimension. We also study the “Stein factorization” of μG,X//G. Namely, let CG,X denote the spectrum of the integral closure of %${\mu_{G,X}^{*}(\mathbb{K}[\mathfrak{g}]^G)}%$ in %${\mathbb{K}(X)^G}%$ . We investigate the structure of the %${\mathfrak{g} //G}%$ -scheme CG,X. Our results partially generalize those obtained by F. Knop for the actions on cotangent bundles and symplectic vector spaces. © Springer-Verlag 2009
abstractGer	Abstract In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X. We study the quotient morphism %${\mu_{G,X}//G : X//G \rightarrow \mathfrak{g} //G}%$ of the moment map %${\mu_{G,X} : X\rightarrow \mathfrak{g}}%$ . We prove that for a wide class of Hamiltonian actions (including, for example, actions on generically symplectic varieties) all fibers of the morphism μG,X//G have the same dimension. We also study the “Stein factorization” of μG,X//G. Namely, let CG,X denote the spectrum of the integral closure of %${\mu_{G,X}^{*}(\mathbb{K}[\mathfrak{g}]^G)}%$ in %${\mathbb{K}(X)^G}%$ . We investigate the structure of the %${\mathfrak{g} //G}%$ -scheme CG,X. Our results partially generalize those obtained by F. Knop for the actions on cotangent bundles and symplectic vector spaces. © Springer-Verlag 2009
abstract_unstemmed	Abstract In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X. We study the quotient morphism %${\mu_{G,X}//G : X//G \rightarrow \mathfrak{g} //G}%$ of the moment map %${\mu_{G,X} : X\rightarrow \mathfrak{g}}%$ . We prove that for a wide class of Hamiltonian actions (including, for example, actions on generically symplectic varieties) all fibers of the morphism μG,X//G have the same dimension. We also study the “Stein factorization” of μG,X//G. Namely, let CG,X denote the spectrum of the integral closure of %${\mu_{G,X}^{*}(\mathbb{K}[\mathfrak{g}]^G)}%$ in %${\mathbb{K}(X)^G}%$ . We investigate the structure of the %${\mathfrak{g} //G}%$ -scheme CG,X. Our results partially generalize those obtained by F. Knop for the actions on cotangent bundles and symplectic vector spaces. © Springer-Verlag 2009
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title_short	Algebraic Hamiltonian actions
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up_date	2024-07-04T00:58:55.149Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR001916076</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327145248.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2009 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00209-009-0587-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR001916076</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00209-009-0587-7-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">Losev, Ivan V.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Algebraic Hamiltonian actions</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2009</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 2009</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X. We study the quotient morphism %${\mu_{G,X}//G : X//G \rightarrow \mathfrak{g} //G}%$ of the moment map %${\mu_{G,X} : X\rightarrow \mathfrak{g}}%$ . We prove that for a wide class of Hamiltonian actions (including, for example, actions on generically symplectic varieties) all fibers of the morphism μG,X//G have the same dimension. We also study the “Stein factorization” of μG,X//G. Namely, let CG,X denote the spectrum of the integral closure of %${\mu_{G,X}^{*}(\mathbb{K}[\mathfrak{g}]^G)}%$ in %${\mathbb{K}(X)^G}%$ . We investigate the structure of the %${\mathfrak{g} //G}%$ -scheme CG,X. Our results partially generalize those obtained by F. Knop for the actions on cotangent bundles and symplectic vector spaces.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Poisson variety</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Reductive group</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hamiltonian action</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Moment map</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Mathematische Zeitschrift</subfield><subfield code="d">Berlin : Springer, 1918</subfield><subfield code="g">263(2009), 3 vom: 14. 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