On equivariant Serre problem for principal bundles

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2018-08-01

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Biswas, Indranil
Dey, Arijit
Poddar, Mainak

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Let E-G be a Gamma-equivariant algebraic principal G-bundle over a normal complex affine variety X equipped with an action of Gamma, where G and Gamma are complex linear algebraic groups. Suppose X is contractible as a topological Gamma-space with a dense orbit, and x(0) is an element of X is a Gamma-fixed point. We show that if Gamma is reductive, then E-G admits a Gamma-equivariant isomorphism with the product principal G-bundle X x rho E-G(x(0)), where rho : Gamma -> G is a homomorphism between algebraic groups. As a consequence, any torus equivariant principal G-bundle over an affine toric variety is equivariantly trivial. This leads to a classification of torus equivariant principal G-bundles over any complex toric variety, generalizing the main result of [A classification of equivariant principal bundles over nonsingular toric, varieties, Internat. J. Math. 27(14) (2016)].

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/66381

Journal

INTERNATIONAL JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.1142/s0129167x18500544

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Natural Sciences and Mathematics, Article

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Citation Formats

I. Biswas, A. Dey, and M. Poddar, “On equivariant Serre problem for principal bundles,” INTERNATIONAL JOURNAL OF MATHEMATICS, pp. 0–0, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/66381.