MOS

Abstract

I will explain a conjectural construction of Bridgeland stability conditions on smooth projective threefolds. It is based on a construction of new t-structures. They produce a stability condition if we assume a conjectural Bogomolov-Gieseker type inequality for the Chern character of certain stable complexes. In this talk, I will present evidence for our conjecture, as well as implications of the conjecture to the birational geometry of threefolds. In particular, it implies a weaker version of Fujita's conjecture. This is based on joint work with Aaron Bertram, Emanuele Macrì and Yukinobu Toda.