Jet schemes of complex plane branches and equisingularity
[Espaces des jets des branches planes complexes et équisingularité]
Mourtada, Hussein1
1 Université de Versailles Saint-Quentin Laboratoire de Mathématiques de Versailles 45 avenue des États-Unis 78035 Versailles CEDEX (France)
Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 2313-2336.

Pour m∈ℕ, nous déterminons les composantes irréductibles des m-èmes espaces des jets d’une branche plane complexe C et nous donnons des formules pour leur nombre N(m) et leurs codimensions, en fonction de m et des générateurs du semigroupe de C. Cette structure des espaces des jets détermine et elle est déterminée par le type topologique de C.

For m∈ℕ, we determine the irreducible components of the m-th Jet Scheme of a complex branch C and we give formulas for their number N(m) and for their codimensions, in terms of m and the generators of the semigroup of C. This structure of the Jet Schemes determines and is determined by the topological type of C.

DOI : 10.5802/aif.2675
Classification : 14E18, 14B05
Keywords: Jet schemes, singularities of plane curves.
Mot clés : espaces des jets, singularités des courbes planes.
Mourtada, Hussein 1

1 Université de Versailles Saint-Quentin Laboratoire de Mathématiques de Versailles 45 avenue des États-Unis 78035 Versailles CEDEX (France) 
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Mourtada, Hussein. Jet schemes of complex plane branches and equisingularity. Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 2313-2336. doi : 10.5802/aif.2675. http://archive.numdam.org/articles/10.5802/aif.2675/

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