Jet schemes of complex plane branches and equisingularity
Annales de l'Institut Fourier, Volume 61 (2011) no. 6, pp. 2313-2336.

For m, 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.

Pour m, 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.

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, Volume 61 (2011) no. 6, pp. 2313-2336. doi : 10.5802/aif.2675. http://www.numdam.org/articles/10.5802/aif.2675/

[1] Abhyankar, Shreeram S. Irreducibility criterion for germs of analytic functions of two complex variables, Adv. Math., Volume 74 (1989), pp. 190-257 | DOI | MR | Zbl

[2] Ein, Lawrence; Lazarsfeld, Robert; Mustaţǎ, Mircea Contact loci in arc spaces, Compos. Math., Volume 140 (2004), pp. 1229-1244 | DOI | MR | Zbl

[3] Garcia Barroso, Evelia Invariants des singularités des courbes planes et courbure de fibre de Milnor, 2004 (Servicio de Publicaciones de la ULL)

[4] Goldin, Rebecca; Teissier, Bernard Resolving singularities of plane analytic branches with one toric morphism, Resolution of singularities (Obergurgl, 1997) (Progr. Math.), Volume 181, Birkhäuser, Basel, 2000, pp. 315-340 | MR | Zbl

[5] Gwoździewicz, Janusz; Płoski, Arkadiusz On the approximate roots of polynomials (Ann. Polon. Math., LX.3, 1995) | Zbl

[6] Igusa, J. On the first terms of certain asymptotic expansions, Complex analysis and algebraic geometry, Iwanami Shoten, Tokyo, 1977, pp. 357-368 | MR | Zbl

[7] Lejeune-Jalabert, Monique; Reguera-López, Ana J. Arcs and wedges on sandwiched surface singularities, Amer. J. Math., Volume 121 (1999) no. 6, pp. 1191-1213 | DOI | MR | Zbl

[8] Merle, M. Invariants polaires des courbes planes, Invent. Math., Volume 41 (1977), pp. 103-111 | DOI | MR | Zbl

[9] Mustaţă, Mircea Jet schemes of locally complete intersection canonical singularities, Invent. Math., Volume 145 (2001), pp. 397-424 (With an appendix by David Eisenbud and Edward Frenkel) | DOI | MR | Zbl

[10] Nash, John F. Jr. Arc structure of singularities, Duke Math. J., Volume 81 (1995), pp. 31-38 | DOI | MR | Zbl

[11] Spivakovsky, Mark Valuations in function fields of surfaces, Amer. J. Math., Volume 112 (1990) no. 1, pp. 107-156 | DOI | MR | Zbl

[12] Vojta, Paul Jets via Hasse-Schmidt derivations, Diophantine geometry (CRM Series), Volume 4, Ed. Norm., Pisa, 2007, pp. 335-361 | MR | Zbl

[13] Zariski, Oscar Studies in equisingularity. I. Equivalent singularities of plane algebroid curves, Amer. J. Math., Volume 87 (1965), pp. 507-536 | DOI | MR | Zbl

[14] Zariski, Oscar Le problème des modules pour les branches planes, École Polytechnique, 1973 (with a appendix by B. Teissier) | MR | Zbl

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