Parametrization of the box variety by theta functions

TL;DR

This paper presents a theta function-based parametrization of the box variety, demonstrating its structure as a modular variety and establishing its definability over the Gauss number field.

Contribution

The authors introduce a novel theta function parametrization of the box variety, linking it to modular forms and number field definitions.

Findings

The box variety is shown to be a modular variety.

Parametrization can be defined over the Gauss number field.

Establishes a new connection between cuboids and modular forms.

Abstract

We describe a parametrization of the box variety (variety of cuboids) by theta functions. This will imply that the box variety is a modular variety. Actually this parametrization can be defined over the Gauss number field.