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

Equivariant sheaves on some spherical varieties

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.
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., (). 

[2]

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

[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.

[4]

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

[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.

[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.

[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.

[8]

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

[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)].

[10]

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

show all references

References:
[1]

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

[2]

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

[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.

[4]

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

[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.

[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.

[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.

[8]

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

[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)].

[10]

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

[1]

Eckhard Meinrenken. Quotients of double vector bundles and multigraded bundles. Journal of Geometric Mechanics, 2021  doi: 10.3934/jgm.2021027

[2]

J. B. van den Berg, J. D. Mireles James. Parameterization of slow-stable manifolds and their invariant vector bundles: Theory and numerical implementation. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4637-4664. doi: 10.3934/dcds.2016002

[3]

V. Kumar Murty, Ying Zong. Splitting of abelian varieties. Advances in Mathematics of Communications, 2014, 8 (4) : 511-519. doi: 10.3934/amc.2014.8.511

[4]

Lawrence Ein, Wenbo Niu, Jinhyung Park. On blowup of secant varieties of curves. Electronic Research Archive, 2021, 29 (6) : 3649-3654. doi: 10.3934/era.2021055

[5]

Anna Go??biewska, S?awomir Rybicki. Equivariant Conley index versus degree for equivariant gradient maps. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 985-997. doi: 10.3934/dcdss.2013.6.985

[6]

Anton Izosimov. Pentagrams, inscribed polygons, and Prym varieties. Electronic Research Announcements, 2016, 23: 25-40. doi: 10.3934/era.2016.23.004

[7]

G. Mashevitzky, B. Plotkin and E. Plotkin. Automorphisms of categories of free algebras of varieties. Electronic Research Announcements, 2002, 8: 1-10.

[8]

A. Giambruno and M. Zaicev. Minimal varieties of algebras of exponential growth. Electronic Research Announcements, 2000, 6: 40-44.

[9]

Laurenţiu Maxim, Jörg Schürmann. Characteristic classes of singular toric varieties. Electronic Research Announcements, 2013, 20: 109-120. doi: 10.3934/era.2013.20.109

[10]

Ghislain Fourier, Gabriele Nebe. Degenerate flag varieties in network coding. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021027

[11]

Jordi-Lluís Figueras, Àlex Haro. Triple collisions of invariant bundles. Discrete and Continuous Dynamical Systems - B, 2013, 18 (8) : 2069-2082. doi: 10.3934/dcdsb.2013.18.2069

[12]

Bas Janssens. Infinitesimally natural principal bundles. Journal of Geometric Mechanics, 2016, 8 (2) : 199-220. doi: 10.3934/jgm.2016004

[13]

V. Balaji, I. Biswas and D. S. Nagaraj. Principal bundles with parabolic structure. Electronic Research Announcements, 2001, 7: 37-44.

[14]

Alexander Barg, Oleg R. Musin. Codes in spherical caps. Advances in Mathematics of Communications, 2007, 1 (1) : 131-149. doi: 10.3934/amc.2007.1.131

[15]

Susanna V. Haziot. On the spherical geopotential approximation for Saturn. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022035

[16]

Thorsten Hüls. Computing stable hierarchies of fiber bundles. Discrete and Continuous Dynamical Systems - B, 2017, 22 (9) : 3341-3367. doi: 10.3934/dcdsb.2017140

[17]

Mauro Patrão, Luiz A. B. San Martin. Morse decomposition of semiflows on fiber bundles. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 561-587. doi: 10.3934/dcds.2007.17.561

[18]

Peter Albers, Jean Gutt, Doris Hein. Periodic Reeb orbits on prequantization bundles. Journal of Modern Dynamics, 2018, 12: 123-150. doi: 10.3934/jmd.2018005

[19]

Jesús Carrillo-Pacheco, Felipe Zaldivar. On codes over FFN$(1,q)$-projective varieties. Advances in Mathematics of Communications, 2016, 10 (2) : 209-220. doi: 10.3934/amc.2016001

[20]

Sylvain E. Cappell, Anatoly Libgober, Laurentiu Maxim and Julius L. Shaneson. Hodge genera and characteristic classes of complex algebraic varieties. Electronic Research Announcements, 2008, 15: 1-7. doi: 10.3934/era.2008.15.1

2020 Impact Factor: 0.929

Metrics

  • PDF downloads (103)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]