Cubic threefolds and abelian varieties of dimension five. II

Details Cubic threefolds and abelian varieties of dimension five. II Cubic threefolds and abelian varieties of dimension five. II

2006-05-25

arxiv.org/abs/math/0605666v2

Mathematics

Algebraic Geometry

16 pages, AMS Latex; shortened version, title changed from "Prym varieties and the Schottky problem for cubic threefolds"

Scientific paper

This paper extends joint work with R. Friedman to show that the closure of the locus of intermediate Jacobians of smooth cubic threefolds, in the moduli space of principally polarized abelian varieties (ppav's) of dimension five, is an irreducible component of the locus of ppav's whose theta divisor has a point of multiplicity three or more. This paper also gives a sharp bound on the multiplicity of a point on the theta divisor of an irreducible ppav of dimension less than or equal to five; for dimensions four and five, this improves the bound due to J. Koll\'ar, R. Smith-R. Varley, and L. Ein-R. Lazarsfeld.

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