This repository contains code to reconstruct a genus 4 curve from its theta constants. See https://arxiv.org/abs/2402.03160 for the accompanying article.
The repo contains two folders:
- magma
- examples
In the Magma folder we have the folowing files:
- auxiliary.m Contains a few auxiliary methods.
- azygetic.m Contains the method that takes a system of four odd azygetic characteristics and extends it to a fundamental system.
- fast_theta.m An adaption of Labrande's fast theta code to compute Theta null values.
- gluingfuncs.m Contains an array of maximal isotropic subgroups of F_2^4 and a few methods that are helpful for gluing.
- good-coordinates.m Contains tools for arithmetic construction from small period matrices
- igusa_quartic.m Reconstruct a genus 2 curve from the fourth powers of the thetas.
- reconstruction.m The main algorithm to reconstruct a genus 4 curve from its theta constants.
- rosenhain.m Compute the Rosenhain invariants of a genus 4 curve from the squares of its theta constants.
- schottky.m Computes the value of the Schottky modular form at a given period matrix tau.
- signs.m Code that uses Riemann's formula to correct the signs of the thetas that has been lost due to taking squares of thetas.
- theta.m Contains methods that compute Theta functions and the Siegel reduction of a period matrix.
In the examples folder we have the following files:
- noam_example.m Constructs a genus 4 curve whose ... TODO