# Invariant theory of $\bigwedge^3(9)$ and genus 2 curves

## TL;DR

This paper extends the geometric invariant theory connection between the third exterior power of a 9-dimensional space and genus 2 curves from complex numbers to arbitrary fields, detailing the necessary arithmetic data for a bijection.

## Contribution

It generalizes previous complex field results to arbitrary fields and characterizes the arithmetic data required for the correspondence.

## Key findings

- Established a bijection over arbitrary fields
- Identified the arithmetic data needed for the correspondence
- Extended the invariant theory connection to broader contexts

## Abstract

Previous work established a connection between the geometric invariant theory of the third exterior power of a 9-dimensional complex vector space and the moduli space of genus 2 curves with some additional data. We generalize this connection to arbitrary fields, and describe the arithmetic data needed to get a bijection between both sides of this story.