Thesis PERÍODOS DE CURVAS GENERALIZADAS DE FERMAT
Date
2018
Authors
TORRES NOVA, YERKO ALEJANDRO
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Abstract
Sean k; n >2 enteros. Una curva generalizada de Fermat de tipo (k; n) es una superficie deRiemann compacta S que admite un subgrupo de automorfismos conformales H < Aut(S)isomorfo a Znk, tal que la superficie cociente S=H tiene n + 1 puntos ramas y cada uno deorden k. Se conoce un modelo algebraico para estos objetos, el cual los hace más sencillode estudiar. Ocupando herramientas de la topología algebraica e integración sobre superficies de Riemann, encontramos un conjunto generador para el primer grupo de homologíade una curva generalizada de Fermat. Finalmente, con esta información, encontramos unconjunto generador para el reticulado de períodos de la variedad Jacobiana asociada.
Let k; n >2 be integers. A generalized Fermat curve of type (k; n) is a compact Riemannsurface S that admits a subgroup of conformal automorphisms H < Aut(S) isomorphicto Znk, such that the quotient surface S=H has n + 1 branch points and each one of orderk. It is known an algebraic model for these objects, which make them easier to study.Using tools from algebraic topology and integration theory on Riemann surfaces, we finda generating set for the first homology group of a generalized Fermat curve. Finally, withthis information, we find a generating set of the period lattice for the asociated Jacobianvariety.
Let k; n >2 be integers. A generalized Fermat curve of type (k; n) is a compact Riemannsurface S that admits a subgroup of conformal automorphisms H < Aut(S) isomorphicto Znk, such that the quotient surface S=H has n + 1 branch points and each one of orderk. It is known an algebraic model for these objects, which make them easier to study.Using tools from algebraic topology and integration theory on Riemann surfaces, we finda generating set for the first homology group of a generalized Fermat curve. Finally, withthis information, we find a generating set of the period lattice for the asociated Jacobianvariety.
Description
Catalogado desde la version PDF de la tesis.
Keywords
CURVAS GENERALIZADAS DE FERMAT , GEOMETRIA COMPLEJA , SUPERFICIES DE RIEMANN , VARIEDAD JACOBIANA