Hessian K3 surfaces of non-Sylvester type

TL;DR

This paper constructs the moduli space of non-Sylvester type cubic surfaces as an arithmetic quotient and determines its modular forms, advancing understanding of their geometric and algebraic properties.

Contribution

It introduces a new construction of the moduli space for non-Sylvester cubic surfaces and explicitly describes their modular form ring.

Findings

Moduli space of non-Sylvester cubic surfaces is an arithmetic quotient.

The graded ring of modular forms of even weights is explicitly determined.

Provides new insights into the structure of these cubic surfaces.

Abstract

We construct the moduli space of cubic surfaces which do not admit a Sylvester form as an arithmetic quotient, and determine the graded ring of modular forms of even weights.