Singularities of base loci on abelian varieties

2025/12/21 by Giuseppe Pareschi, Pareschi, Giuseppe
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Tensor decomposition and applications

paper · doi:10.48550/arxiv.2512.18919

openalex publication_date 2025/12/21 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

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 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.

Citations

• Higher multiplier ideals
• Singularities of divisors of small degrees on abelian varieties
• Derived invariance of the Albanese relative canonical ring
• Characterizing Jacobians via the KP equation and via flexes and degenerate trisecants to the Kummer variety: an algebro-geometric approach
• The Fourier-Mukai transform made easy
• Hodge ideals
• Hodge modules on complex tori and generic vanishing for compact Kähler manifolds
• Regularity on abelian varieties III: relationship with Generic Vanishing and applications
• GV-sheaves, Fourier-Mukai transform, and Generic Vanishing
• Singularities of divisors of low degree on abelian varieties
• A derived category approach to generic vanishing
• Fourier transforms, generic vanishing theorems and polarizations of abelian varieties
• Singularities of Theta Divisors, and the Birational Geometry of Irregular Varieties

Related

• The Equations of Singular Loci of Ample Divisors on (Subvarieties of) Abelian Varieties
• Asymptotic base loci on singular varieties
• Singularities of linear systems and boundedness of Fano varieties
• Log canonical thresholds, F-pure thresholds, and non-standard extensions
• Log canonical thresholds on varieties with bounded singularities