Intersection theory and Chern classes on normal varieties

TL;DR

This paper extends intersection theory and Chern class concepts to normal varieties, establishing new inequalities and boundedness results in positive characteristic.

Contribution

It generalizes Mumford's intersection theory to higher dimensions and defines the second Chern class for reflexive sheaves on normal varieties.

Findings

Established Bogomolov type inequalities in positive characteristic.

Proved new boundedness results for normal varieties.

Extended intersection theory to higher-dimensional normal varieties.

Abstract

We study intersection theory and Chern classes of reflexive sheaves on normal varieties. In particular, we define generalization of Mumford's intersection theory on normal surfaces to higher dimensions. We also define and study the second Chern class for reflexive sheaves on normal varieties. We use these results to prove some Bogomolov type inequalities on normal varieties in positive characteristic. We also prove some new boundedness results on normal varieties in positive characteristic.