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 thi...
- Autores:
-
Pérez Bernal, Juan Martín
- Tipo de recurso:
- 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/
| Summary: | 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. |
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