On the Abel-Jacobi maps of Fermat Jacobians

2010/03/01 by Noriyuki Otsubo, Otsubo, Noriyuki · 1 citation
Computer Science · Mathematics · #14C25 #33C20 #33C65 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1003.0357

openalex publication_date 2010/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Abel-Jacobi image of the Ceresa cycle W_k-W_k^-, where W_k is the image of the k-th symmetric product of a curve X on its Jacobian variety. For the Fermat curve of degree N, we express it in terms of special values of generalized hypergeometric functions and give a criterion for the non-vanishing of W_k-W_k^- modulo algebraic equivalence, which is verified numerically for some N and k.

Citations

• On the regulator of Fermat motives and generalized hypergeometric functions

Cited by

• The modified diagonal cycles of Hypergeometric curves

Related

• Nontrivial algebraic cycles in the Jacobian varieties of some quotients of Fermat curves
• Cycles in Jacobians: infinitesimal results
• A Generalized Torelli Theorem
• Ceresa Cycles of X₀(N)
• The modified diagonal cycles of Hypergeometric curves