Numerical reconstruction of curves from their Jacobians

2021/03/04 by Daniele Agostini, Türkü Özlüm Çelik, Agostini, Daniele +3
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #Polynomial and algebraic computation #Robotic Path Planning Algorithms

paper · pdf · doi:10.48550/arxiv.2103.03138

openalex publication_date 2021/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Deforming curves in jacobians to non-jacobians I: curves in C⁽²⁾
• Reconstruction of curves from their theta hyperplanes in genera 6 and 7
• On the Jacobian Scheme of a plane curve
• A Torelli theorem for curves over finite fields
• Computing isogenies between Jacobian of curves of genus 2 and 3