Stability conditions on threefolds with vanishing Chern classes

TL;DR

This paper proves a key inequality for threefolds with special geometric properties, establishing Bridgeland stability conditions and confirming conjectures across different characteristics.

Contribution

It extends the Bogomolov-Gieseker inequality to threefolds with vanishing Chern classes in all characteristics, enabling new stability results and applications.

Findings

Proved the Bogomolov-Gieseker type inequality for threefolds with vanishing Chern classes.

Established the existence of Bridgeland stability conditions on these threefolds.

Confirmed Fujita's conjecture and derived a Reider type theorem for such threefolds.

Abstract

We prove the Bogomolov-Gieseker type inequality conjectured by Bayer, Macri and Toda for threefolds with semistable tangent bundles and vanishing Chern classes in any characteristic, which was originally proved by Bayer, Macri and Stellari in characteristic zero. This gives the existence of Bridgeland stability conditions on such threefolds. As applications, we obtain Reider type theorem and confirm Fujita's conjecture for such threefolds in any characteristic.