An ampleness criterion for rank 2 vector bundles on surfaces

TL;DR

This paper develops an ampleness criterion for globally generated rank 2 vector bundles on surfaces, adapting the Bogomolov stable restriction theorem, with applications to Lazarsfeld-Mukai bundles and line congruences.

Contribution

It introduces a new ampleness criterion for rank 2 vector bundles on surfaces based on the Bogomolov stable restriction theorem, expanding understanding of vector bundle positivity.

Findings

Provides an ampleness criterion for certain rank 2 bundles

Applies to Lazarsfeld-Mukai bundles and line congruences

Suggests potential for constructing surfaces with ample cotangent bundle

Abstract

We observe that the proof of the Bogomolov stable restriction theorem can be adapted to give an ampleness criterion for globally generated rank 2 vector bundles on certain surfaces. This applies to the Lazarsfeld-Mukai bundles, to congruences of lines in P^3, and possibly to the construction of surfaces with ample cotangent bundle (help welcome!).