The loci of abelian varieties with points of high multiplicity on the theta divisor

Details The loci of abelian varieties with points of high multiplicity on the theta divisor The loci of abelian varieties with points of high multiplicity on the theta divisor

2008-05-27

arxiv.org/abs/0805.4148v1

Mathematics

Algebraic Geometry

Scientific paper

We study the loci of principally polarized abelian varieties with points of high multiplicity on the theta divisor. Using the heat equation and degeneration techniques, we relate these loci and their closures to each other, as well as to the singular set of the universal theta divisor. We obtain bounds on the dimensions of these loci and relations among their dimensions, and make further conjectures about their structure.

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