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

Samuel Grushevsky; Riccardo Salvati Manni

doi:10.1007/s10711-008-9326-1

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

Samuel Grushevsky
, Riccardo Salvati Manni

Simons Center for Geometry & Physics

University of Rome La Sapienza

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Pages (from-to)	233-247
Number of pages	15
Journal	Geometriae Dedicata
Volume	139
Issue number	1
DOIs	https://doi.org/10.1007/s10711-008-9326-1
State	Published - Apr 2009

Keywords

Abelian variety
Singularities
Theta divisor
Theta function

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10.1007/s10711-008-9326-1

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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.",

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AU - Salvati Manni, Riccardo

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N2 - 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.

AB - 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.

KW - Abelian variety

KW - Singularities

KW - Theta divisor

KW - Theta function

UR - https://www.scopus.com/pages/publications/61449117729

U2 - 10.1007/s10711-008-9326-1

DO - 10.1007/s10711-008-9326-1

M3 - Article

AN - SCOPUS:61449117729

SN - 0046-5755

VL - 139

SP - 233

EP - 247

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -

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

Abstract

Keywords

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