A cohomological interpretation of Bogomolov's instability

TL;DR

This paper provides a new proof of Bogomolov's instability theorem and links it to a cohomological condition involving the non-vanishing of the first cohomology group of a divisor.

Contribution

It introduces a cohomological perspective on Bogomolov's instability, establishing an equivalence with a cohomology non-vanishing condition.

Findings

New proof of Bogomolov's instability theorem

Equivalence between instability and cohomology non-vanishing

Cohomological characterization of divisor properties

Abstract

We give a new proof of Bogomolov's instability theorem. Furthermore we prove that it is equivalent to a statement which characterizes when the first cohomology group of a suitable divisor does not vanish.