Group actions on local moduli space of holomorphic vector bundles

TL;DR

This paper demonstrates that actions of complex reductive Lie groups on holomorphic vector bundles over compact complex manifolds can be locally extended to their local moduli spaces, revealing new insights into the symmetry properties of these geometric structures.

Contribution

It establishes the local extendability of reductive Lie group actions to the moduli space of holomorphic vector bundles, a novel result in complex geometry.

Findings

Actions extend locally to moduli space

Reductive Lie groups play a key role

Enhances understanding of symmetry in vector bundles

Abstract

We prove that actions of complex reductive Lie groups on a holomorphic vector bundle over a complex compact manifold are locally extendable to its local moduli space.