Microlocal versal deformations of the plane curves $ {y}^{k}={x}^{n}$

Cabral, João; Neto, Orlando

doi:10.1016/j.crma.2009.10.026

Analytic Geometry

Microlocal versal deformations of the plane curves

y^{k} = x^{n}

[Déformations verselles microlocales des courbes planes

y^{k} = x^{n}

]

Présenté par : Étienne Ghys

Cabral, João ¹ ; Neto, Orlando ²

¹ CMAF and Departamento de Matemática, Universidade de Lisboa, 2829-516 Caparica, Portugal
² CMAF and Departamento de Matemática, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal

Comptes Rendus. Mathématique, Tome 347 (2009) no. 23-24, pp. 1409-1414.

Résumé
Abstract

On introduit la notion de déformation verselle microlocale d'un germe de courbe plane. Nous construisons la déformation verselle équisingulière du conormal d'un germe de courbe plane irréductible semi-quasi-homogène.

We introduce the notion of microlocal versal deformation of a plane curve. We construct equisingular versal deformations of Legendrian curves that are the conormal of a semi-quasi-homogeneous branch.

Reçu le : 2008-04-22
Accepté le : 2009-10-29
Publié le : 2009-11-10

DOI : 10.1016/j.crma.2009.10.026

Affiliations des auteurs :

Cabral, João ¹ ; Neto, Orlando ²

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     title = {Microlocal versal deformations of the plane curves $ {y}^{k}={x}^{n}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1409--1414},
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Cabral, João; Neto, Orlando. Microlocal versal deformations of the plane curves $ {y}^{k}={x}^{n}$. Comptes Rendus. Mathématique, Tome 347 (2009) no. 23-24, pp. 1409-1414. doi : 10.1016/j.crma.2009.10.026. http://www.numdam.org/articles/10.1016/j.crma.2009.10.026/

Bibliographie
Cité par

[1] A. Araújo, O. Neto, Moduli of Legendrian curves, Ann. Fac. Sci. Toulouse Math., in press

[2] Greuel, G.M.; Lossen, C.; Shustin, E. Introduction to Singularities and Deformations, Springer, 2007

[3] Gunning, R.; Rossi, H. Analytic Functions of Several Complex Variables, Prentice-Hall, 1965

[4] Kas, A.; Schlessinger, M. On the versal deformation of a complex space with an isolated singularity, Math. Ann., Volume 196 (1972), pp. 23-29

[5] Sato, M.; Kashiwara, T.; Kimura, M.; Oshima, T. Microlocal analysis of prehomogeneous vector spaces, Invent. Math., Volume 62 (1980), pp. 117-179

[6] Wall, C.T.C. Singular Points of Plane Curves, London Math. Society, 2004

Cité par Sources :

^☆ This research was partially supported by FEDER and FCT-Plurianual 2009.