The loci of abelian varieties with points of high multiplicity on the theta divisor |
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Authors: | Samuel Grushevsky Riccardo Salvati Manni |
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Affiliation: | (1) Mathematics Department, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA;(2) Dipartimento di Matematica, Università “La Sapienza”, Piazzale A. Moro 2, Rome, 00185, Italy |
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Abstract: | 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. Research of the first author is supported in part by National Science Foundation under the grant DMS-05-55867. |
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Keywords: | Abelian variety Theta divisor Theta function Singularities |
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