Algebraic Geometry Seminar: "The monodromy of generalized Kummer varieties"

Eyal Markman, University of Massachusetts -- Amherst

Abstract: A generalized Kummer variety of dimension 2n is the fiber of the Albanese map from the Hilbert scheme of n+1 points on an abelian surface to the surface. We compute the monodromy group of a generalized Kummer variety via equivalences of derived categories of abelian surfaces. As an application we prove the Hodge conjecture for the generic abelian fourfold of Weil type with complex multiplication by an arbitrary imaginary quadratic field, but with trivial discriminant. The latter result is inspired by a recent observation of O'Grady that the third intermediate Jacobians of smooth projective varieties of generalized Kummer deformation type form complete families of abelian fourfolds of Weil type.

Host: Matt Kerr