On projective space bundle with nef normalized tautological divisor

TL;DR

This paper investigates the structure of projective space bundles with nef normalized tautological divisors and characterizes abelian varieties through their relation to these bundles.

Contribution

It provides a new structural understanding of such bundles and offers a characterization of abelian varieties up to finite étale cover.

Findings

Characterization of abelian varieties via projective space bundles

Structural results on bundles with nef normalized tautological divisor

Insights into the geometry of bundles with nef relative anti-canonical line bundle

Abstract

In this paper, we study the structure of projective space bundles whose relative anti-canonical line bundle is nef. As an application, we get a characterization of abelian varieties up to finite etale covering.