Bogomolov's inequality and Higgs sheaves on normal varieties in positive characteristic

TL;DR

This paper extends Bogomolov's inequality and restriction theorems to Higgs sheaves on normal varieties in positive characteristic, providing new boundedness results and redefining Higgs sheaves in this context.

Contribution

It proves Bogomolov's inequality on normal projective varieties in positive characteristic and redefines Higgs sheaves on normal varieties, establishing new restriction theorems and inequalities.

Findings

Proved Bogomolov's inequality in positive characteristic

Established new restriction theorems for Higgs sheaves

Derived boundedness results for Higgs sheaves

Abstract

We prove Bogomolov's inequality on a normal projective variety in positive characteristic and we use it to show some new restriction theorems and a new boundedness result. Then we redefine Higgs sheaves on normal varieties and we prove restriction theorems and Bogomolov type inequalities for semistable logarithmic Higgs sheaves on some normal varieties in an arbitrary characteristic.