Cubic threefolds and abelian varieties of dimension five. II
نویسنده
چکیده
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 (ppavs) of dimension five, is an irreducible component of the locus of ppavs 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 indecomposable ppav of dimension less than or equal to five; for dimensions four and five, this improves the bound due to J. Kollár, R. Smith-R. Varley, and L. Ein-R. Lazarsfeld.
منابع مشابه
Cubic Threefolds and Abelian Varieties of Dimension Five
Cubic threefolds have been studied in algebraic geometry since classical times. In [5], Clemens and Griffiths proved that the intermediate Jacobian JX of a smooth cubic threefold is not isomorphic as a principally polarized abelian variety to a product of Jacobians of curves, which implies the irrationality of X. They also established the Torelli theorem for cubic threefolds: the principally po...
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