Geometriae Dedicata

, Volume 139, Issue 1, pp 233–247 | Cite as

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

Original Paper

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.

Keywords

Abelian variety Theta divisor Theta function Singularities 

Mathematics Subject Classification (2000)

14K25 11F46 14H42 14K10 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Mathematics DepartmentPrinceton UniversityPrincetonUSA
  2. 2.Dipartimento di MatematicaUniversità “La Sapienza”RomeItaly

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