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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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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.