March 3, 2026Open Access

Singularities of base loci on abelian varieties

Key Points

The log canonical threshold of the base ideal is proven to be greater than or equal to one in abelian varieties.
Equality occurs only if the base locus contains divisorial components, establishing a unique condition.
The research highlights similar assertions for ideals from translates of theta divisors and finite subgroup actions.
Understanding these relationships may deepen insights into the geometry of abelian varieties, suggesting further exploration.

Abstract

We prove that the log canonical threshold of the base ideal of a complete linear system on a complex abelian variety is 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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Authors

Giuseppe Pareschi

Journals

Rendiconti Lincei Matematica e Applicazioni

Actions

Institutions

University of Rome Tor Vergata

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Singularities of base loci on abelian varieties

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

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