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Title: Resoluciones minimales de curvas monomiales
Author: Borja Gutiérrez, Cristian
Director/Tutor: Zarzuela, Santiago
Keywords: Corbes el·líptiques
Treballs de fi de grau
Varietats abelianes
Funcions zeta
Elliptic curves
Bachelor's thesis
Abelian varieties
Zeta functions
Computer software
Issue Date: 20-Jun-2019
Abstract: [en] We study the graded free resolutions in the polynomial ring giving results of existence, uniqueness and finitude. We study the correspondence between the monomial curves and the associated numerical semigroup that will allow us, using several results about resolutions, to fnd explicitly the structure of the free resolution of any monomial curve in the 3 dimensional affine space. To arrive at these results, we do a basic study of the categories of graded rings and semigroups. In addition, a way to calculate effectively the parameters necessary to find these resolutions is given by means of basic results on Diophantine equations.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Santiago Zarzuela
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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