Multiplicities of irreducible theta divisors

2020/02/11 by Victor Lozovanu, Lozovanu, Victor
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2002.04360

openalex publication_date 2020/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (A,Θ) be a complex principally polarized abelian variety of dimension g≥ 4. Based on vanishing theorems, differentiation techniques and intersection theory, we show that whenever the theta divisor Θ is irreducible, its multiplicity at any point is at most g-2. This improves work of Kollár, Smith-Varley, and Ein-Lazarsfeld. We also introduce some new ideas to study the same type of questions for pluri-theta divisors.

Citations

• Vanishing theorems and the multigraded regularity of nonsingular subvarieties
• Singular divisors and syzygies of polarized abelian threefolds

Related

• The loci of abelian varieties with points of high multiplicity on the theta divisor
• Geometry of theta divisors --- a survey
• Singularities of the theta divisor at points of order two
• Points of order two on theta divisors
• The Moduli Space of Abelian Varieties and the Singularities of the Theta Divisor