Bridgeland stability conditions on some threefolds of general type

TL;DR

This paper establishes Bridgeland stability conditions on certain threefolds of general type by proving a Bogomolov-Gieseker type inequality for products of three curves, using advanced techniques in algebraic geometry.

Contribution

It provides the first examples of Bridgeland stability conditions on some threefolds of general type, expanding the understanding of stability conditions in complex geometry.

Findings

Proved the Bogomolov-Gieseker type inequality for products of three curves.

Established Bridgeland stability conditions on some threefolds of general type.

Utilized spreading out technique, Frobenius morphism, and positive characteristic inequalities.

Abstract

We prove the Bogomolov-Gieseker type inequality conjectured by Bayer, Macri and Toda for some products of three curves. This gives the first examples of Bridgeland stability conditions on some threefolds of general type. The key ingredients are the spreading out technique, Frobenius morphism and Bogomolov's inequality for product type varieties in positive characteristic, proved by the author recently.