The primitive cohomology of the theta divisor of an abelian fivefold

2013/11/25 by E. Izadi, Elham Izadi, Cs. Tamas +5
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14C30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #math.AG #msc:14C30

paper · pdf · doi:10.48550/arxiv.1311.6212

59 pages

arxiv created 2013/11/25 · openalex publication_date 2013/11/25 · arxiv updated 2013/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The primitive cohomology of the theta divisor of a principally polarized abelian variety of dimension g is a Hodge structure of level g-3. The Hodge conjecture predicts that it is contained in the image, under the Abel-Jacobi map, of the cohomology of a family of curves in the theta divisor. In this paper we use the Prym map to show that this version of the Hodge conjecture is true for the theta divisor of a general abelian fivefold.

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