Strong Bogomolov inequalities and ample divisors on moduli spaces of sheaves
Speaker: Jack Huizenga, Penn State
Abstract: The existence problem for semistable sheaves on a surface seeks to classify the possible numerical invariants of a semistable sheaf. In other words, for what numerical invariants is the moduli space of semistable sheaves nonempty? The classical Bogomolov inequality says that any semistable sheaf has nonnegative discriminant, so this is one restriction on the possible numerical invariants. Strong Bogomolov inequalities are refinements which further restrict the possible invariants; they often have interesting number-theoretic or combinatorial structure, related to the geometry of rigid bundles. In this talk I will explain a close relationship between such inequalities and the computation of cones of ample divisors on moduli spaces of sheaves with large discriminant. This is joint work with Izzet Coskun.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm