Modular forms of degree two and curves of genus two in characteristic two

TL;DR

This paper explores the structure of degree two modular forms in characteristic two by examining their connection with genus two curves, providing insights into their algebraic properties.

Contribution

It introduces a new description of the ring of modular forms of degree two in characteristic two through its relation with genus two curves.

Findings

Characterization of the ring of modular forms in characteristic two

Relation between modular forms and genus two curves in characteristic two

Structural insights into modular forms in special characteristic

Abstract

We describe the ring of modular forms of degree 2 in characteristic 2 using its relation with curves of genus 2.