A degree bound for globally generated vector bundles

TL;DR

This paper establishes a precise degree bound for globally generated vector bundles on projective varieties and applies it to derive a Del Pezzo-Bertini type theorem for subvarieties of Grassmannians.

Contribution

It provides a sharp degree bound for globally generated vector bundles and extends classical theorems to subvarieties of Grassmannians.

Findings

Sharp degree bound for globally generated vector bundles

Del Pezzo-Bertini type theorem for Grassmannian subvarieties

Applications to varieties of minimal degree

Abstract

We obtain a sharp bound on the degree of a globally generated vector bundle over a reduced irreducible projective variety defined over an algebraically closed field of characteristic zero. As an application, we obtain a Del Pezzo-Bertini type theorem on varieties of minimal degree for subvarieties of Grassmannians.