Degeneration of Prym Varieties: a Computational Approach to the Indeterminacy Locus of the Prym Map and Degenerations of Cubic Threefolds

Graduate Thesis Or Dissertation

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Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/6w924b840

Abstract

In this paper we will explore the extension of the Prym period map from the moduli space of admissible double covers of stable curves to the perfect cone compactification of the moduli space of principally polarized abelian varieties. We will use the insight from Casalaina-Martin, Grushevsky, Hulek, Laza, and Dutour Sikirić to understand the indeterminacy locus of this extension of the Prym map. Using computational methods we characterize the indeterminacy locus up to codimension 10 in the case where the base curves have genus 5. The last section will be devoted to an application of the Prym period map in which we construct the necessary extension data needed to classify the intermediate Jacobian of a cubic threefold with 2A₁ singularity type.

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