Kuznetsov components of derived categories and constructions of stability conditions on them (II)
Tzu-Yang Chou (University of Edinburgh, UK)
2022-12-29 13:30 - 14:30
Room 440, Astronomy and Mathematics Building
In the first talk we introduced the Kuznetsov components and proved a general method to construct an induced stability condition on a semiorthogonal component. In this talk, we will focus on one of its applications: the existence of Bridgeland stability conditions on Kuznetsov components of smooth Fano threefolds. We will assume some technical results such as Bogomolov-Gieseker inequality, and then construct a weak stability on the derived category of coherent sheaves satisfying the assumptions of the theorem (whereas the existence of stability conditions is known, they may not descend to Ku in general), which consists of a rotation of stability function and a double tilted heart. Finally we will apply this to Fano threefolds of index one and low genus as an example to exhibit why we need the double tilt and how we choose the torsion pair.