Stability conditions in the trivial canonical bundle case: Hilbert schemes of points


The construction of stability conditions on the bounded derived category of coherent sheaves on smooth projective varieties is notoriously a difficult problem. In this talk, I will review some results and techniques related to this problem. I will specifically concentrate on the case of Hilbert schemes of points on K3 surfaces and on generic abelian varieties of any dimension. This is joint work in progress with C. Li, E. Macrì and P. Stellari.