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.
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Published online:
João Cabral 1; Orlando Neto 2
@article{CRMATH_2009__347_23-24_1409_0, author = {Jo\~ao Cabral and Orlando Neto}, title = {Microlocal versal deformations of the plane curves $ {y}^{k}={x}^{n}$}, journal = {Comptes Rendus. Math\'ematique}, pages = {1409--1414}, publisher = {Elsevier}, volume = {347}, number = {23-24}, year = {2009}, doi = {10.1016/j.crma.2009.10.026}, language = {en}, }
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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.10.026/
[1] A. Araújo, O. Neto, Moduli of Legendrian curves, Ann. Fac. Sci. Toulouse Math., in press
[2] Introduction to Singularities and Deformations, Springer, 2007
[3] Analytic Functions of Several Complex Variables, Prentice-Hall, 1965
[4] On the versal deformation of a complex space with an isolated singularity, Math. Ann., Volume 196 (1972), pp. 23-29
[5] Microlocal analysis of prehomogeneous vector spaces, Invent. Math., Volume 62 (1980), pp. 117-179
[6] Singular Points of Plane Curves, London Math. Society, 2004
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☆ This research was partially supported by FEDER and FCT-Plurianual 2009.
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