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.
Pareschi, G. (2025). Singularities of base loci on abelian varieties. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 36(2), 365-375 [10.4171/rlm/1088].
Singularities of base loci on abelian varieties
Giuseppe Pareschi
2025-01-01
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.File in questo prodotto:
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