Bridgeland Stability Conditions on Fano Threefolds

Abstract

We show the existence of Bridgeland stability conditions on all Fano threefolds, by proving a modified version of a conjecture by Bayer, Toda, and the second author. The key technical ingredient is a strong Bogomolov inequality, proved recently by Chunyi Li. Additionally, we prove the original conjecture for some toric threefolds by using the toric Frobenius morphism.

Keywords

• mathematics - algebraic geometry
• 14f05 (primary), 14j30, 18e30 (secondary)