Introduction to Elliptic Quasi-Modular Forms via Moduli Spaces

TL;DR

This paper provides a rigorous introduction to elliptic quasi-modular forms using moduli spaces and the Gauss-Manin connection, highlighting their historical significance in mirror symmetry as studied by Dijkgraaf.

Contribution

It offers a concise, rigorous exposition of elliptic quasi-modular forms through moduli spaces and the Gauss-Manin connection, connecting to their role in mirror symmetry.

Findings

Clarifies the structure of elliptic quasi-modular forms.

Links quasi-modular forms to mirror symmetry via Dijkgraaf's work.

Provides a rigorous mathematical framework for the theory.

Abstract

In this paper we present rigorously and as succintly as possible the theory of elliptic quasi-modular forms by means of moduli spaces and the Gauss-Manin connection, and deal with one of the main historical appearances of quasi-modular forms, which was the seminal case of mirror symmetry treated by Dijkgraaf.