Equivariant principal bundles on nonsingular toric varieties
Arijit Dey, Mainak Poddar

TL;DR
This paper classifies equivariant principal G-bundles on nonsingular toric varieties with Abelian G, showing they always split and providing explicit parametrizations for certain cases.
Contribution
It introduces a classification framework for equivariant principal G-bundles on nonsingular toric varieties and demonstrates their splitting property, with explicit parametrizations for specific G and varieties.
Findings
Any equivariant principal G-bundle splits into a reduction to a torus intersection.
Provides explicit parametrization of isomorphism classes for complete varieties.
Establishes a classification for bundles with Abelian structure groups.
Abstract
We give a classification of the equivariant principal -bundles on a nonsingular toric variety when is a closed Abelian subgroup of . We prove that any such bundle splits, that is, admits a reduction of structure group to the intersection of with a torus. We give an explicit parametrization of the isomorphism classes of such bundles for a large family of when is complete.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Alkaloids: synthesis and pharmacology · Advanced Algebra and Geometry
