Singularities of base loci on abelian varieties

We prove that the log canonical threshold of the base ideal of a complete linear system on a complex abelian variety is \ge 1 , and that equality holds if and only if the base locus has divisorial components. Consequently, the same assertions hold for the ideal of the intersection of translates of theta divisors by the points of a finite subgroup.

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Publication Details

Journal
Rendiconti Lincei Matematica e Applicazioni
Published
2026-02-17
DOI
https://doi.org/10.4171/rlm/1088
Primary Topic
Commutative Algebra and Its Applications
Type
article
Field-Weighted Citation Impact
0.00

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article

Singularities of base loci on abelian varieties

Giuseppe Pareschi
Rendiconti Lincei Matematica e Applicazioni
Commutative Algebra and Its Applications
article

Singularities of base loci on abelian varieties

Giuseppe Pareschi
article en

Abstract

We prove that the log canonical threshold of the base ideal of a complete linear system on a complex abelian variety is \ge 1 , and that equality holds if and only if the base locus has divisorial components. Consequently, the same assertions hold for the ideal of the intersection of translates of theta divisors by the points of a finite subgroup.

Rendiconti Lincei Matematica e ApplicazioniVol. 36(2)
University of Rome Tor Vergata (IT)
Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca, Università degli Studi di Roma Tor Vergata, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni
Openalex Percentile: Top 48%
Commutative Algebra and Its Applications
DOIOpen Access PDFOpenAlex
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