On automorphism groups of fiber bundles

TL;DR

This paper extends classical automorphism group results to holomorphic fiber bundles within the framework of group schemes and explores automorphism lifting properties for torsors under abelian varieties.

Contribution

It introduces new analogues of classical automorphism results for holomorphic fiber bundles in the context of group schemes and studies automorphism lifting for abelian variety torsors.

Findings

Automorphism groups of holomorphic fiber bundles are characterized in the group scheme setting.

A lifting property for connected automorphism groups of torsors under abelian varieties is established.

Applications to homogeneous bundles over abelian varieties are discussed.

Abstract

We obtain analogues of classical results on automorphism groups of holomorphic fiber bundles, in the setting of group schemes. Also, we establish a lifting property of the connected automorphism group, for torsors under abelian varieties. These results will be applied to the study of homogeneous bundles over abelian varieties.