On F-pure thresholds: computations and relations to others invariants
The main object in this thesis is the F-pure threshold associated to a polynomial f. This threshold is a rational number in [0,1], with smaller values that suggest worse singularities for the hypersurface defined by the equation f = 0. First, we will present in a general way the relation between the...
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| Formato: | tesis de maestría |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | México |
| Recursos: | Centro de Investigación en Matemáticas |
| Repositorio: | Repositorio Institucional CIMAT |
| OAI Identifier: | oai:cimat.repositorioinstitucional.mx:1008/1010 |
| Acesso em linha: | http://cimat.repositorioinstitucional.mx/jspui/handle/1008/1010 |
| Access Level: | acceso abierto |
| Palavra-chave: | info:eu-repo/classification/MSC/F-pure thresholds info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/12 info:eu-repo/classification/cti/1299 info:eu-repo/classification/cti/129999 |
| Resumo: | The main object in this thesis is the F-pure threshold associated to a polynomial f. This threshold is a rational number in [0,1], with smaller values that suggest worse singularities for the hypersurface defined by the equation f = 0. First, we will present in a general way the relation between the main concept with Log-canonical threshold, and Bernstein-Sato polynomials. Then, we are going to show several examples of these relations. Particularly, we are going to compute the F-pure threshold of a Thom-Sebastiani-type sum, and the F-pure threshold of a determinantal ideal of maximal size. Finally, we will use the Fpure threshold to find and compare roots of Bernstein-Sato polynomials. |
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