A classification of equivariant principal bundles over nonsingular toric varieties

TL;DR

This paper classifies equivariant principal G-bundles over nonsingular toric varieties, showing trivializations over affine cases and providing splitting results, advancing understanding of bundle structures in algebraic geometry.

Contribution

It provides a comprehensive classification of equivariant principal bundles over nonsingular toric varieties, including trivialization and splitting results, which were previously not fully understood.

Findings

Any equivariant principal G-bundle over an affine nonsingular toric variety is trivial in the equivariant sense.

The paper establishes splitting results for these bundles.

A complete classification scheme for such bundles is developed.

Abstract

We classify holomorphic as well as algebraic torus equivariant principal $G$-bundles over a nonsingular toric variety $X$, where $G$ is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric variety admits a trivialization in equivariant sense. We also obtain some splitting results.