TANNAKIAN CLASSIFICATION OF EQUIVARIANT PRINCIPAL BUNDLES ON TORIC VARIETIES

2020-03-01
Biswas, Indranil
Dey, Arijit
Poddar, Mainak
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.
Citation Formats
I. Biswas, A. Dey, and M. Poddar, “TANNAKIAN CLASSIFICATION OF EQUIVARIANT PRINCIPAL BUNDLES ON TORIC VARIETIES,” pp. 0–0, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/67099.