TANNAKIAN CLASSIFICATION OF EQUIVARIANT PRINCIPAL BUNDLES ON TORIC VARIETIES

Date

2020-03-01

Author

Biswas, Indranil
Dey, Arijit
Poddar, Mainak

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LetXbe a complete toric variety equipped with the action of a torusT, andGa reductive algebraic group, defined over an algebraically closed fieldK. We introduce the notion of a compatible n-ary sumation -filtered algebra associated toX, generalizing the notion of a compatible n-ary sumation -filtered vector space due to Klyachko, where n-ary sumation denotes the fan ofX. We combine Klyachko's classification ofT-equivariant vector bundles onXwith Nori's Tannakian approach to principalG-bundles, to give an equivalence of categories betweenT-equivariant principalG-bundles onXand certain compatible n-ary sumation -filtered algebras associated toX, when the characteristic ofKis 0.

Subject Keywords

Geometry and Topology, Algebra and Number Theory

URI

https://hdl.handle.net/11511/67099

Journal

TRANSFORMATION GROUPS

DOI

https://doi.org/10.1007/s00031-020-09557-5

Collections

Natural Sciences and Mathematics, Article

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Citation Formats

I. Biswas, A. Dey, and M. Poddar, “TANNAKIAN CLASSIFICATION OF EQUIVARIANT PRINCIPAL BUNDLES ON TORIC VARIETIES,” TRANSFORMATION GROUPS, pp. 0–0, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/67099.