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  2011, 18: 119-130. doi: 10.3934/era.2011.18.119

Equivariant sheaves on some spherical varieties

Aravind Asok 1, and  James Parson 2,

1. 

Department of Mathematics, University of Southern California, Los Angeles, CA, 90089, United States
2. 

Department of Mathematics, Hood College, Frederick, MD 21701, United States

Received  October 2010 Revised  July 2011 Published  September 2011

We provide a concrete description of the category of equivariant vector bundles on a class of spherical $\G$-varieties.
Keywords: stacks, Equivariant vector bundles, spherical varieties, descent..
Mathematics Subject Classification: Primary: 14M17; Secondary: 14J6.
Citation: Aravind Asok, James Parson. Equivariant sheaves on some spherical varieties. Electronic Research Announcements, 2011, 18: 119-130. doi: 10.3934/era.2011.18.119
References:
[1]

A. Asok and J. Parson, Equivariant sheaves on spherical varieties,, in preparation., ().   Google Scholar

[2]

A. Asok, Equivariant vector bundles on certain affine $G$-varieties, Pure Appl. Math. Q., 2 (2006), 1085-1102.  Google Scholar

[3]

M. Demazure and P. Gabriel, "Groupes Algébriques. Tome I: Géométrie Algébrique, Généralités, Groupes Commutatifs," Avec un appendice Corps de classes local par Michiel Hazewinkel, Masson & Cie, Éditeur, Paris, North-Holland Publishing Co., Amsterdam, 1970.  Google Scholar

[4]

J. Giraud, Méthode de la descente, Bull. Soc. Math. France Mém., 2 (1964), viii+150.  Google Scholar

[5]

S. Kato, Equivariant vector bundles on group completions, J. Reine Angew. Math., 581 (2005), 71-116. doi: 10.1515/crll.2005.2005.581.71.  Google Scholar

[6]

A. A. Klyachko, Equivariant bundles over toric varieties, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 53 (1989), 1001-1039, 1135, translation in Math. USSR-Izv., 35 (1990), 337-375. doi: 10.1070/IM1990v035n02ABEH000707.  Google Scholar

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F. Knop, "The Luna-Vust Theory of Spherical Embeddings," Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989), 225-249, Manoj Prakashan, Madras, 1991.  Google Scholar

[8]

F. Knop, The asymptotic behavior of invariant collective motion, Invent. Math., 116 (1994), 309-328. doi: 10.1007/BF01231563.  Google Scholar

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Revêtements étales et groupe fondamental (SGA 1), Documents Mathématiques (Paris) [Mathematical Documents (Paris)], 3, Société Mathématique de France, Paris, 2003, Séminaire de géométrie algébrique du Bois Marie 1960-61 [Algebraic Geometry Seminar of Bois Marie 1960-61], Directed by A. Grothendieck, With two papers by M. Raynaud, Updated and annotated reprint of the 1971 original [Lecture Notes in Math., 224, Springer, Berlin; MR0354651 (50 \#7129)].  Google Scholar

[10]

D. Timashev, "Homogeneous Spaces and Equivariant Embeddings," Encyclopaedia of Mathematical Sciences, 138, Invariant Theory and Algebraic Transformation Groups, 8, Springer, Heidelberg, 2011.  Google Scholar

show all references

References:
[1]

A. Asok and J. Parson, Equivariant sheaves on spherical varieties,, in preparation., ().   Google Scholar

[2]

A. Asok, Equivariant vector bundles on certain affine $G$-varieties, Pure Appl. Math. Q., 2 (2006), 1085-1102.  Google Scholar

[3]

M. Demazure and P. Gabriel, "Groupes Algébriques. Tome I: Géométrie Algébrique, Généralités, Groupes Commutatifs," Avec un appendice Corps de classes local par Michiel Hazewinkel, Masson & Cie, Éditeur, Paris, North-Holland Publishing Co., Amsterdam, 1970.  Google Scholar

[4]

J. Giraud, Méthode de la descente, Bull. Soc. Math. France Mém., 2 (1964), viii+150.  Google Scholar

[5]

S. Kato, Equivariant vector bundles on group completions, J. Reine Angew. Math., 581 (2005), 71-116. doi: 10.1515/crll.2005.2005.581.71.  Google Scholar

[6]

A. A. Klyachko, Equivariant bundles over toric varieties, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 53 (1989), 1001-1039, 1135, translation in Math. USSR-Izv., 35 (1990), 337-375. doi: 10.1070/IM1990v035n02ABEH000707.  Google Scholar

[7]

F. Knop, "The Luna-Vust Theory of Spherical Embeddings," Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989), 225-249, Manoj Prakashan, Madras, 1991.  Google Scholar

[8]

F. Knop, The asymptotic behavior of invariant collective motion, Invent. Math., 116 (1994), 309-328. doi: 10.1007/BF01231563.  Google Scholar

[9]

Revêtements étales et groupe fondamental (SGA 1), Documents Mathématiques (Paris) [Mathematical Documents (Paris)], 3, Société Mathématique de France, Paris, 2003, Séminaire de géométrie algébrique du Bois Marie 1960-61 [Algebraic Geometry Seminar of Bois Marie 1960-61], Directed by A. Grothendieck, With two papers by M. Raynaud, Updated and annotated reprint of the 1971 original [Lecture Notes in Math., 224, Springer, Berlin; MR0354651 (50 \#7129)].  Google Scholar

[10]

D. Timashev, "Homogeneous Spaces and Equivariant Embeddings," Encyclopaedia of Mathematical Sciences, 138, Invariant Theory and Algebraic Transformation Groups, 8, Springer, Heidelberg, 2011.  Google Scholar

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