A Babylonian tower theorem for principal bundles over projective spaces

TL;DR

This paper extends the Babylonian tower theorem from vector bundles to principal G-bundles over projective spaces, providing new structural insights into these bundles over algebraically closed fields.

Contribution

It generalizes the theorem to principal G-bundles, offering novel understanding of their structure over projective spaces.

Findings

Generalization of the Babylonian tower theorem to principal G-bundles

New structural insights into principal G-bundles

Extension over algebraically closed fields

Abstract

We generalise the variant of the Babylonian tower theorem for vector bundles on projective spaces proved by I. Coanda and G. Trautmann (2006) to the case of principal $G$-bundles over projective spaces, where $G$ is a linear algebraic group defined over an algebraically closed field. In course of the proofs some new insight into the structure of such principal $G$-bundles is obtained.