Limits of quotients of polynomial functions of three variables, Classification of G-graded twisted algebras and the computation of the F-rational locus

This thesis is divided in three main parts. In the first part we provide a theoretical method to determine the existence of the limit of a quotient of polynomial functions of three variables. An algorithm to compute such limits in the case where the polynomials have rational coeffcients, or more generally, coefficients in a real finite extension of the rational numbers is also described. In the second part, for any finite abelian group G, we present an exact formula to count the G graded twisted algebras satisfying certain symmetry condition. Finally, in the third part we describe an algorithm to compute the F-rational locus of an affine algebra over a field of prime characteristic p 0 by computing first its global test ideal. As a consequence we deduce the Openness of the F-rational locus, a result originally proved in [27]

• Autores: Hernández Rodas, Juan Pablo
• Tipo de recurso: Doctoral thesis
• Fecha de publicación: 2015
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/54927
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/54927; http://bdigital.unal.edu.co/50191/
• Palabra clave: 51 Matemáticas / Mathematics; G-graded twisted algebras; Limits of rational functions of three varibles; F-rational locus
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional