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

João Cabral; Orlando Neto

doi:10.1016/j.crma.2009.10.026

Analytic Geometry

Microlocal versal deformations of the plane curves

y^{k} = x^{n}

Presented by: Étienne Ghys

João Cabral ¹; Orlando Neto ²

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

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

Abstract (Original language)
Résumé

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.

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.

Received: 2008-04-22
Accepted: 2009-10-29
Published online: 2009-11-10

DOI: 10.1016/j.crma.2009.10.026

Author's affiliations:

João Cabral ¹ ; Orlando Neto 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

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     author = {Jo\~ao Cabral and Orlando Neto},
     title = {Microlocal versal deformations of the plane curves $ {y}^{k}={x}^{n}$},
     journal = {Comptes Rendus. Math\'ematique},
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     year = {2009},
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     doi = {10.1016/j.crma.2009.10.026},
     language = {en},
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João Cabral; Orlando Neto. Microlocal versal deformations of the plane curves $ {y}^{k}={x}^{n}$. Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1409-1414. doi: 10.1016/j.crma.2009.10.026

References
Cited by

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

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

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

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

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

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

Cited by Sources:

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

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