Effective reconstruction of generic genus 4 curves from their theta hyperplanes

Abstract

Effective reconstruction formulas of a curve from its theta hyperplanes are known classically in genus 2 (where the theta hyperplanes are Weierstrass points), and 3 (where, for a generic curve, the theta hyperplanes are bitangents to a plane quartic). However, for higher genera, no formula or algorithm are known. In this paper we give an explicit (and simple) algorithm for computing a generic genus 4 curve from it's theta hyperplanes.

no content modification to previous version; presentation modification following referees comments

References in corpus (2)

• Any smooth plane quartic can be reconstructed from its bitangents
• Formulas for the arithmetic geometric mean of curves of genus 3

Cited by in corpus (4)

• Two-Torsion Subgroups of some Modular Jacobians
• Effective reconstruction of generic genus 5 curves from their theta hyperplanes
• Crossing the transcendental divide: from translation surfaces to algebraic curves
• A compactification of the moduli space of multiple-spin curves