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| HAL : hal-00308807, version 2 |
| arXiv : 0808.0158 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (01-08-2008) | v2 (26-01-2012) |
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| APPROXIMATE ROOTS, TORIC RESOLUTIONS AND DEFORMATIONS OF A PLANE BRANCH |
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| Pedro Daniel Gonzalez Perez 1 |
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| (01/08/2008) |
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| We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial $f$ 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 $f$. As a consequence we find out a Kouchnirenko type formula for the Milnor number $(C,0)$. Our results provide a geometrical approach to Abhyankar's straight line conditions and its consequences. As an application we give an equisingularity criterion for a family of plane curves to be equisingular to a plane branch and we express it algorithmically. |
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| 1 : | DPTO. ALGEBRA UCM (UCM) |
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Universidad Complutense de Madrid |
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| Domaine | : | Mathématiques/Géométrie algébrique |
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| approximate roots – deformations of a plane curve – equisingularity criterion |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00308807, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00308807 | |
| oai:hal.archives-ouvertes.fr:hal-00308807 | |
| Contributeur : Pedro Daniel Gonzalez Perez | |
| Soumis le : Jeudi 26 Janvier 2012, 13:37:39 | |
| Dernière modification le : Jeudi 26 Janvier 2012, 16:41:50 | |
