The irreducible components of the primal cohomology of the theta divisor of an abelian fivefold

2015/09/30 by Elham Izadi, Jie Wang, Izadi, Elham +1
Mathematics · #14C30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1510.00046

openalex publication_date 2015/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The primal cohomology \mathbbK_ℚ of the theta divisor Θ of a principally polarized abelian fivefold (ppav) is the direct sum of its invariant and anti-invariant parts \mathbbK_ℚ⁺¹, resp. \mathbbK_ℚ^-1 under the action of -1. For smooth Θ, these have dimension 6 and 72 respectively. We show that \mathbbK_ℚ⁺¹ consists of Hodge classes and, for a very general ppav, \mathbbK_ℚ^-1 is a simple Hodge structure of level 2.

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