Global deformations of certain rational almost homogeneous projective bundles

TL;DR

This paper investigates how certain rational projective bundles over projective spaces can be deformed globally, revealing that deformations over P^1 preserve bundle structure, while in higher dimensions, some bundles can deform into non-almost homogeneous manifolds.

Contribution

It demonstrates that projective bundles over P^1 maintain their structure under global deformations, and constructs higher-dimensional examples of Fano bundles that deform into non-almost homogeneous manifolds.

Findings

Deformations over P^1 preserve the projective bundle structure.

Existence of higher-dimensional Fano bundles deforming into non-almost homogeneous manifolds.

Construction of explicit examples in dimensions ≥ 3.

Abstract

We study global deformations of certain projective bundles over projective spaces. We show that any projective global deformation of a projective bundle over $\bP^1$ carries the structure of a projective bundle over some projective space. Furthermore, we construct examples in arbitrary dimension $\ge 3$ of almost homogeneous Fano projective bundles over $\bP^2$ which can be globally deformed to non-almost homogeneous manifolds.