On a numerical characterization of non-simple principally polarized abelian varieties

2015/07/30 by Robert Auffarth, Auffarth, Robert
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.1507.08618

Some typos fixed. Accepted for publication in Mathematische Zeitschrift

openalex publication_date 2015/07/30 · arxiv created 2015/10/04 · arxiv updated 2015/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To every abelian subvariety of a principally polarized abelian variety (A, L) we canonically associate a numerical class in the Néron-Severi group of A. We prove that these classes are characterized by their intersection numbers with L; moreover, the cycle class induced by an abelian subvariety in the Chow ring of A modulo algebraic equivalence can be described in terms of its numerical divisor class. Over the field of complex numbers, this correspondence gives way to an explicit description of the (coarse) moduli space that parametrizes non-simple principally polarized abelian varieties with a fixed numerical class.

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