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 gen...
- 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
| Summary: | 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] |
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