Algebraic Geometry Seminar

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Irreducible symplectic varieties via relative Prym varieties

Speaker: Sasha Viktorova, KU Leuven

Location: Warren Weaver Hall 512

Date: Tuesday, October 22, 2024, 3:30 p.m.

Synopsis:

In this talk we present a construction of irreducible symplectic varieties (which are singular analogues of Hyperkähler manifolds). We start by fixing a K3 surface S with an antisymplectic involution i. For a choice of a smooth ample curve C on the quotient S/i, one can construct the corresponding compactified relative Prym variety. The variety P is a (singular) Largangian fibration over the linear system of C. By the work of Arbarello, Saccà and Ferretti, we know that if S/i is an Enriques surface, then P is an irreducible symplectic variety. Inspired by this result and an earlier work of Markushevich and Tikhomirov, we investigate the situation when S/i is a rational surface and find sufficient conditions to ensure that P is an irreducible symplectic variety. This is joint work with E. Brakkee, C. Camere, A. Grossi, L. Pertusi and G. Saccà.