A non-hyperelliptic curve with torsion Ceresa class

TL;DR

This paper presents a specific example of a non-hyperelliptic genus 3 curve for which the Ceresa cycle class in the intermediate Jacobian is torsion, providing insight into algebraic cycles on Jacobians.

Contribution

It constructs an explicit non-hyperelliptic genus 3 curve with a torsion Ceresa cycle class, advancing understanding of algebraic cycles in algebraic geometry.

Findings

The Ceresa cycle class for the constructed curve is torsion.

The example demonstrates non-hyperelliptic curves with torsion Ceresa classes.

Provides new evidence on the structure of algebraic cycles in Jacobians.

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.