A non-hyperelliptic curve with torsion Ceresa cycle modulo algebraic equivalence

TL;DR

This paper presents a specific genus 3 non-hyperelliptic curve where the Ceresa cycle class is torsion in the Jacobian modulo algebraic equivalence, highlighting a special geometric property.

Contribution

It constructs an explicit example of a non-hyperelliptic genus 3 curve with a torsion Ceresa cycle class in its Jacobian, a novel instance in algebraic geometry.

Findings

The Ceresa cycle class is torsion in the Jacobian.

The curve is explicitly non-hyperelliptic of genus 3.

Provides insight into the structure of Ceresa cycles.

Abstract

We exhibit a non-hyperelliptic curve C of genus 3 such that the class of the Ceresa cycle [C]-[(-1)*C] in JC modulo algebraic equivalence is torsion.