Non-commutative abelian surfaces II: applications

Location: 11th Floor Lecture Hall Speaker Laura Pertusi, Università degli Studi di Milano Session Chair Anthony Várilly-Alvarado, Rice University Abstract This is the second of two lectures which illustrate a new construction of noncommutative deformations of abelian surfaces with applications in hyperkahler geometry and Hodge theory. Using the theory of stability conditions in families of smooth and proper linear categories, we describe every locally complete family of hyperkahler manifolds deformation equivalent to a generalized Kummer variety, out of moduli spaces of stable objects in noncommutative abelian surfaces. Next we apply our construction to provide a shorter proof of the algebricity of Hodge-Weil classes on Weil type abelian fourfolds of discriminant 1. Based on a joint work with in preparation with Arend Bayer, Alex Perry and Xiaolei Zhao.