The Bogomolov-Gieseker-Koseki inequality on surfaces with canonical singularities in arbitrary characteristic

TL;DR

This paper extends the Bogomolov-Gieseker inequality to projective surfaces with canonical singularities over fields of any characteristic, broadening its applicability and related classical results.

Contribution

It generalizes the inequality and its classical applications to surfaces with canonical singularities in arbitrary characteristic.

Findings

Extended the inequality to surfaces with canonical singularities

Generalized classical applications of the inequality

Applicable in arbitrary characteristic fields

Abstract

This note generalizes the celebrated Bogomolov-Gieseker inequality for smooth projective surfaces over an algebraically closed field of characteristic zero to projective surfaces in arbitrary characteristic with canonical singularities. We also generalize to this context some classical applications of the Bogomolov-Gieseker inequality.