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arXiv · 1806.02526

Tannakian classification of equivariant principal bundles on toric varieties

Indranil Biswas·Arijit Dey·Mainak Poddar
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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 $\Sigma$--filtered algebra associated to $X$, generalizing the notion of a compatible $\Sigma$--filtered vector space due to Klyachko, where $\Sigma$ 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 $\Sigma$--filtered algebras associated to $X$, when the characteristic of $K$ is $0$.

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Indranil Biswas, Arijit Dey, Mainak Poddar. 2018-06-07. Tannakian classification of equivariant principal bundles on toric varieties. https://arxiv.org/abs/1806.02526

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