The moduli stack of elliptic curves

By moduli space of Riemann surfaces of genus g, where g is a non-negative integer, we mean the set of isomorphism classes of complex analytic structures on a closed oriented surface of genus g, fixed once and for all. It is not clear \textit{a priori} why this definition makes sense, nor whether this set has an extra structure, turning it into some kind of \textit{space}. In this memoir, we focus on these questions in the genus 1 case. As a matter of fact, we shall also fix some extra data: a base point on our genus 1 curve. The moduli space we obtain by doing this is called the moduli space of elliptic curves and the goal of the thesis is to show that this space is a complex analytic space, in a sense that we will make precise along the way.

• Autores: Pérez Bernal, Juan Martín
• Fecha de publicación: 2019
• Institución: Universidad de los Andes
• Repositorio: Séneca: repositorio Uniandes
• Idioma: eng
• OAI Identifier: oai:repositorio.uniandes.edu.co:1992/43725
• Acceso en línea: http://hdl.handle.net/1992/43725
• Palabra clave: Superficies de Riemann - Investigaciones; Isomorfismo (Matemáticas) - Investigaciones; Espacios analíticos - Investigaciones; Matemáticas
• Rights: openAccess
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/