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Math-Physics Joint Seminar

Monday, November 11, 2019 - 3:15pm

Eyal Markman

University of Massachussetts at Amherst


University of Pennsylvania

DRL 4N30

joint Algebra/Math-Physics seminar, note the special time and place

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.