We approach the Torelli problem of recostructing a curve from its Jacobian from a computational point of view. Following Dubrovin, we design a machinery to solve this problem effectively, which builds on methods in numerical algebraic geometry. We verify this methods via numerical experiments with curves up to genus 7.

We approach the Torelli problem of reconstructing a curve from its Jacobian from a computational point of view. Following Dubrovin, we design machinery to solve this problem effectively, which builds on methods in numerical algebraic geometry. We verify this method via numerical experiments with curves up to genus 7.