On uniform flag bundles on Fano manifolds

TL;DR

This paper extends the theory of uniform vector bundles on Fano manifolds to uniform principal bundles, using associated flag bundles to analyze their geometric properties and establish foundational theorems.

Contribution

It introduces the study of uniform principal bundles on Fano manifolds via flag bundles, providing new theoretical results that parallel existing vector bundle theories.

Findings

Developed background for uniform principal bundles

Proved theorems relating flag bundles to uniform principal bundles

Extended vector bundle results to principal bundle context

Abstract

As a natural extension of the theory of uniform vector bundles on Fano manifolds, we consider uniform principal bundles, and study them by means of the associated flag bundles, as their natural projective geometric realizations. In this paper we develop the necessary background, and prove some theorems that are flag bundle counterparts of some of the central results in the theory of uniform vector bundles.