Equivariant bundles and connections

TL;DR

This paper studies the conditions necessary for principal bundles over complex manifolds with a group action to admit compatible equivariance structures, enhancing understanding of symmetry in complex geometry.

Contribution

It provides new criteria for when principal bundles on complex manifolds with group actions can be endowed with equivariance structures, advancing the theory of equivariant bundles.

Findings

Established necessary and sufficient conditions for equivariance of principal bundles.

Connected group actions to the existence of compatible bundle structures.

Contributed to the classification of equivariant principal bundles on complex manifolds.

Abstract

Let $X$ be a connected complex manifold equipped with a holomorphic action of a complex Lie group $G$. We investigate conditions under which a principal bundle on $X$ admits a $G$--equivariance structure.