Movable curves and semistable sheaves

TL;DR

This paper generalizes results on slope-semistable sheaves to movable curve classes, leading to new flatness criteria for reflexive sheaves on singular varieties and a characterization of finite quotients of Abelian varieties.

Contribution

It extends classical semistability results to movable curve classes and provides new flatness and characterization results for sheaves and varieties.

Findings

New flatness results for reflexive sheaves on singular varieties

Characterization of finite quotients of Abelian varieties via Chern class conditions

Extension of semistability theory to movable curve classes

Abstract

This paper extends a number of known results on slope-semistable sheaves from the classical case to the setting where polarisations are given by movable curve classes. As applications, we obtain new flatness results for reflexive sheaves on singular varieties, as well as a characterisation of finite quotients of Abelian varieties via a Chern class condition.