The moduli space of Hessian quartic surfaces and automorphic forms

TL;DR

This paper demonstrates the existence of 15 automorphic forms of weight 8 on the moduli space of marked Hessian quartic surfaces, linking them to the coefficients of the Sylvester form of cubic surfaces.

Contribution

It establishes the existence of specific automorphic forms on the moduli space and relates them to classical invariants of cubic surfaces.

Findings

15 automorphic forms of weight 8 are constructed.

Automorphic forms are interpreted via Sylvester form coefficients.

Results connect moduli space geometry with algebraic invariants.

Abstract

We shall show the existence of 15 automorphic forms of weight 8 on the moduli space of marked Hessian quartic surfaces of cubic surfaces. These automorphic forms can be interpreted in terms of the coefficients of the Sylvester form of a general cubic surface.