Restriction of stable bundles on a jacobian of genus 2 to an embedded curve

TL;DR

This paper investigates how stable rank 2 vector bundles on a genus 2 Jacobian restrict to the embedded genus 2 curve, analyzing the properties of the restriction map between their moduli spaces.

Contribution

It describes the restriction map from the moduli space of stable rank 2 bundles on a genus 2 Jacobian to that on the embedded genus 2 curve, providing new insights into their relationship.

Findings

Characterization of the restriction map between moduli spaces

Conditions under which bundles restrict to stable bundles on the curve

Insights into the structure of stable bundles on Jacobians and curves

Abstract

The aim of this note is to describe the restriction map from the moduli space of stable rank 2 bundle with small $c_2$ on a jacobian $X$ of dimension 2, to the moduli space of stable rank 2 bundles on the corresponding genus 2 curve $C$ embedded in $X$.