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 number field K, but with trivial

discriminant invariant. 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.

### Math-Physics Joint Seminar

Monday, November 11, 2019 - 3:15pm

#### Eyal Markman

University of Massachussetts at Amherst