Note on curves in a Jacobian

1992/02/17 by Elisabetta Colombo, Bert van Geemen, Colombo, Elisabetta +1 · 2 citations
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9202015

18 pages, Latex 2.09

openalex publication_date 1992/02/17 · arxiv created 1992/02/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a curve C, viewed as a cycle in its Jacobian, we study its image n_*C under multiplication by n on JC. We prove that the subgroup generated by these cycles, in the Chow group modulo algebraic equivalence, has rank at most d-1, where d is the gonality of C. We also discuss some general facts on the action of n_* on the Chow groups.

Cited by

• On Modified Diagonal Cycles and the Beauville Decomposition of the Ceresa Cycle
• The modified diagonal cycles of Hypergeometric curves

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