Jet schemes of complex plane branches and equisingularity

[Espaces des jets des branches planes complexes et équisingularité]

Mourtada, Hussein

Annales de l'Institut Fourier, Tome 61 (2011), p. 2313-2336 / Harvested from Numdam

Résumé

Pour $m \in \mathbb{N}$, 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 $C.$

Abstract

For $m \in \mathbb{N}$, 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 $C$.

Détail

Publié le : 2011-01-01

MR 2976313 | Zbl 1247.14011

DOI : https://doi.org/10.5802/aif.2675
Classification:  14E18,  14B05
Mots clés: espaces des jets, singularités des courbes planes.

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