Approximate roots, toric resolutions and deformations of a plane branch
We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial f is an element of C{x}[y], defining a plane branch (C, 0), in the light of the toric embedded resolution of the branch. This leads to the definition of a class of (non-equisingular) deformations of a plane branc...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/42247 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/42247 |
| Access Level: | acceso abierto |
| Palabra clave: | 512.76/.77 512.745.2 Generalized Tschirnhausen transformation Newton-Puiseux expansion hypersurface singularities polar invariants curves irreducibility approximate roots deformations of a plane curve equisingularity criterion Álgebra 1201 Álgebra |
| Sumario: | We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial f is an element of C{x}[y], defining a plane branch (C, 0), in the light of the toric embedded resolution of the branch. This leads to the definition of a class of (non-equisingular) deformations of a plane branch (C, 0) supported on certain monomials in the approximate roots of f, which are essential in the study of Harnack smoothings of real plane branches by Risler and the author. Our results provide also a geometrical approach to Abhyankar's irreducibility criterion for power series in two variables and also a criterion to determine if a family of plane curves is equisingular to a plane branch. |
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