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Calabi-Yau Threefolds and Moduli of Abelian Surfaces I

Mark Gross·Sorin Popescu
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Abstract

We describe birational models and decide the rationality/unirationality of moduli spaces AA_{d} (and AA^{lev}_{d}) of (1,d)-polarized abelian surfaces (with canonical level structure, respectively) for small values of d. The projective lines identified in the rational/unirational moduli spaces correspond to pencils of abelian surfaces traced on nodal threefolds living naturally in the corresponding ambient projective spaces, and whose small resolutions are new Calabi-Yau threefolds with Euler characteristic zero.

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Mark Gross, Sorin Popescu. 2000-01-14. Calabi-Yau Threefolds and Moduli of Abelian Surfaces I. https://arxiv.org/abs/math/0001089

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