# Effective reconstruction of generic genus 5 curves from their theta hyperplanes

## TL;DR

This paper presents a method to reconstruct generic genus 5 curves from their theta hyperplanes, providing a complete description of the Schottky locus in genus 5 through effective computational techniques.

## Contribution

It introduces an effective reconstruction method for genus 5 curves from theta hyperplanes and describes the Schottky locus explicitly using this data.

## Key findings

- Successful reconstruction of genus 5 curves from theta hyperplanes
- Complete description of the Schottky locus in genus 5
- Use of certified numerical algorithms for proof

## Abstract

We effectively reconstruct the set of enveloping quadrics of a generic curve C of genus 5 from its theta hyperplanes; for a generic genus 5 curve C this data suffices to effectively reconstruct C. As a consequence we get a complete description of the Schottky locus in genus 5 in terms of theta hyperplanes. The computational part of the proof is a certified numerical argument.