Algebraic cycles on Jacobian varieties

2002/04/15 by Arnaud Beauville, Beauville, Arnaud · 1 citation
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.math/0204188

8 pages

arxiv created 2002/04/15 · openalex publication_date 2002/04/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let J be the Jacobian of a smooth curve C of genus g, and let A(J) be the ring of algebraic cycles modulo algebraic equivalence on J, tensored with Q. We study in this paper the smallest Q-vector subspace R of A(J) which contains C and is stable under the natural operations of A(J) : intersection and Pontryagin products, pull back and push down under multiplication by integers. We prove that this "tautological subring" is generated (over Q) by the classes of the subvarieties W₁=C, W₂=C+C, ..., W_g-1. If C admits a morphism of degree d onto P¹, we prove that the last d-1 classes suffice.

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• Tautological Cycles on Jacobian Varieties

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