Some equations for the universal Kummer variety

TL;DR

This paper introduces a method to derive quartic Heisenberg invariant equations for Kummer varieties, providing explicit examples and new modular forms that relate to the moduli space of Riemann surfaces.

Contribution

It presents a novel approach to find invariant equations for Kummer varieties and identifies new modular forms of lower weight for genus 5.

Findings

New equations for g-dimensional Kummer varieties

Explicit examples of these equations

Discovery of new modular forms of lower weight for g=5

Abstract

We give a method to find quartic Heisenberg invariant equations for Kummer varieties and we give some explicit examples. From these equations for g-dimensional Kummer varieties one obtains equations for the moduli space of g+1-dimensional Kummer varieties. These again define modular forms which vanish on the period matrices of Riemann surfaces. The modular forms that we find for g=5 appear to be new and of lower weight than known before.