Edoardo Mason: Cohomology of general stable sheaves on numerically K-trivial surfaces

Abstract: In this talk we will report on recent progress on the problem of computing the cohomology groups of a stable coherent sheaf which is general in its moduli space. This problem is the first step of the generalization to higher dimension of the classical Brill–Noether theory for curves and it was studied by Coskun, Nuer and Yoshioka in the case of K3 and abelian surfaces, while in this talk we will discuss recent developments for bielliptic and Enriques surfaces, the latter case being a joint work in progress with Papallo, Piskunov, Vacca and Yu. Our methods rely on the theory of Bridgeland stability conditions on the derived category of sheaves on a surface.