Bridgeland Stability Conditions on Fano Threefolds
  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. 
Marcello Bernardara, Emanuele Macr\`i, Benjamin Schmidt, Xiaolei Zhao
math.AG