EVENT DETAILS AND ABSTRACT

Title: Stability conditions in families and families of Hyperkähler varieties
Speaker: Howard Nuer
Speaker Info: UIC
Brief Description:
Special Note:
Abstract:

In this talk, I describe a new construction of families of Hyperkähler varieties associated to families of cubic fourfolds. Our construction is based on crucial technical progress in the theory of Bridgeland stability conditions on derived categories of algebraic varieties. More specifically, we develop a notion of a ``family of stability conditions'' on a family of varieties, as well as a version of that for families with Kuznetsov subcategories of the derived categories of the fibers; both come with a notion of relative moduli spaces of stable objects. Our construction allows us to prove analogues of the powerful results for moduli spaces of stable sheaves on K3 surfaces, due to Mukai, Huybrechts, O'Grady, Yoshioka and others, in the setting of cubic fourfolds. We also obtain as a corollary the invariance of Piyaratne-Toda’s generalized Donaldson-Thomas invariants under smooth deformations of the underlying Calabi-Yau 3-folds. The talk is based on joint work with Bayer, Macri, Lahoz, Perry, and Stellari.