Joe Foster (U Oregon)
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PDL C-38
Title: Moduli spaces of sheaves on Weil-type abelian fourfolds
Abstract: Generalized Kummer varieties constitute one of the two known examples of compact hyper-Kaehler varieties that occur in each even complex dimension. They are constructed as albanese fibers of moduli spaces of sheaves on an abelian surface. However, they exhibit more deformations than the underlying abelian surface. Remarkably, these "hidden" deformations of generalized Kummer varieties are encoded in the deformation theory of Weil-type abelian fourfolds with discriminant one. This behooves the study of moduli spaces of sheaves on Weil-type abelian fourfolds with the objective of recovering a complete family of generalized Kummer varieties. In this talk, I will describe a construction of such moduli spaces. As a corollary, we provide a novel proof of the Hodge conjecture for Weil-type abelian fourfolds of discriminant one. This work is joint with Nicolas Addington.
Pre-seminar: I will provide an introduction to the theory of compact hyper-Kaehler (or irreducible holomorphic symplectic) varieties of generalized Kummer deformation type, with an eye towards the relationship between their deformation theory and the deformation theory of abelian varieties.