An extension of Fujita's non extendability theorem for Grassmannians

TL;DR

This paper investigates the geometric properties of certain complex projective varieties containing Grassmannians, proving that specific vector bundles associated with these varieties cannot be ample, thus extending Fujita's non-extendability theorem.

Contribution

It extends Fujita's non-extendability theorem by showing that the rank two nef vector bundle defining the Grassmannian zero locus cannot be ample.

Findings

The vector bundle E cannot be ample.

The variety X contains a Grassmannian G(1,r) as a zero locus.

Extension of Fujita's theorem to new geometric contexts.

Abstract

In this paper we study smooth complex projective varieties $X$ containing a Grassmannian of lines $G(1,r)$ which appears as the zero locus of a section of a rank two nef vector bundle $E$. Among other things we prove that the bundle $E$ cannot be ample.