Modular forms of weight 3m and elliptic modular surface

TL;DR

This paper establishes a natural isomorphism between the graded ring of modular forms of weights divisible by 3 and a log canonical ring associated with the elliptic modular surface, linking modular forms to algebraic geometry.

Contribution

It introduces a novel connection between modular forms of specific weights and the log canonical ring of elliptic modular surfaces.

Findings

Proves the isomorphism between modular form rings and log canonical rings.

Provides a new geometric interpretation of modular forms of weight divisible by 3.

Enhances understanding of the structure of modular forms in algebraic geometry.

Abstract

We prove that the graded ring of modular forms of weight divisible by 3 is naturally isomorphic to a certain log canonical ring of the corresponding elliptic modular surface.