Algebraic Geometry Seminar

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The Prym Map Revisited

Speaker: Klaus Hulek, Leibniz Universität Hannover

Location: Warren Weaver Hall 201

Date: Tuesday, February 10, 2015, 3:30 p.m.

Synopsis:

It was already shown by Friedman and Smith that the Prym map does not extend as a regular morphism from the moduli space R_g+1 of admissible covers to the second Voronoi compactification of the moduli space A_g of principally polarized abelian varieties. Due to work of Alexeev, Birkenhake and Hulek as well as Vologodsky it is known that the indeterminacy locus of this map is the closure of the so-called Friedman-Smith loci. Motivated by work of Alexeev and Brunyate, we investigate the Prym map to other torioidal compactifications of A_g, in particular the perfect cone compactification. For this we develop a systematic approach, which separates the geometric aspects from the combinatorial issues and reduces the problem to the computation of certain monodromy cones. This approach was motivated by and can be applied to the study of the map which associates to a cubic threefold its intermediate Jacobian. This is joint work with Sebastian Casalaina-Martin, Samuel Grushevsky and Radu Laza.