Abstract

We exhibit a non-hyperelliptic curve C of genus 3 such that the class of the Ceresa cycle [C]-[-C] in the intermediate Jacobian of JC is torsion.

Highlights

  • Let C be a complex curve of genus g ≥ 3, and p a point of C

  • If C is hyperelliptic zp (C ) is algebraically trivial – it is zero if one chooses for p a Weierstrass point

  • Not much is known besides these two extreme cases

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Summary

Introduction

Let C be a complex curve of genus g ≥ 3, and p a point of C . The Ceresa cycle zp (C ) is the cycle [C ] − [(−1J )∗C ] in the Chow group C H1(J )hom of homologically trivial 1-cycles. The Ceresa class cp (C ) is the image of zp (C ) in the intermediate Jacobian J1(J ) parameterizing 1-cycles under the Abel–Jacobi map C H1(J )hom → J1(J ). When C is general, zp (C ) is not algebraically trivial [2].

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