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TANNAKIAN CLASSIFICATION OF EQUIVARIANT PRINCIPAL BUNDLES ON TORIC VARIETIES
I. Biswas, M. Poddar
Published in
2020
Volume: 25

Issue: 4
Pages: 1009 - 1035
Abstract
Let X be a complete toric variety equipped with the action of a torus T, and G a reductive algebraic group, defined over an algebraically closed field K. We introduce the notion of a compatible ∑-filtered algebra associated to X, generalizing the notion of a compatible ∑-filtered vector space due to Klyachko, where ∑ denotes the fan of X. We combine Klyachko's classification of T-equivariant vector bundles on X with Nori's Tannakian approach to principal G-bundles, to give an equivalence of categories between T-equivariant principal G-bundles on X and certain compatible ∑-filtered algebras associated to X, when the characteristic of K is 0. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.