Calabi-Yau Threefolds and Moduli of Abelian Surfaces I

Details Calabi-Yau Threefolds and Moduli of Abelian Surfaces I Calabi-Yau Threefolds and Moduli of Abelian Surfaces I

2000-01-14

arxiv.org/abs/math/0001089v1

Mathematics

Algebraic Geometry

56 pages, 2 figures, plain TeX, uses diagrams.tex and epsf.tex

Scientific paper

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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