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TANNAKIAN CLASSIFICATION OF EQUIVARIANT PRINCIPAL BUNDLES ON TORIC VARIETIES

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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.

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India

    INDRANIL BISWAS

  2. Department of Mathematics, Indian Institute of Technology-Madras, Chennai, India

    ARIJIT DEY

  3. Mathematics Group Middle East Technical University Northern Cyprus Campus Guzelyurt, Mersin 10, Turkey

    MAINAK PODDAR

  4. Department of Mathematics, Indian Institute of Science Education and Research (IISER), Pune, India

    MAINAK PODDAR

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  1. INDRANIL BISWAS
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  2. ARIJIT DEY
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  3. MAINAK PODDAR
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Correspondence to MAINAK PODDAR.

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BISWAS, I., DEY, A. & PODDAR, M. TANNAKIAN CLASSIFICATION OF EQUIVARIANT PRINCIPAL BUNDLES ON TORIC VARIETIES. Transformation Groups 25, 1009–1035 (2020). https://doi.org/10.1007/s00031-020-09557-5

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