The Saito module and the moduli of a germ of curve in (ℂ 2 ,0).
[Le module de Saito et les modules d’un germe de courbe de (ℂ 2 ,0)]
Genzmer, Yohann1
1 Institut de Mathématiques de Toulouse, 118, route de Narbonne, 31062 Toulouse Cedex 09 (France)
Annales de l'Institut Fourier, Online first, 55 p.

Cet article est une étude des espaces de module d’une courbe S dans le plan complexe, c’est-à-dire, de la classe d’équisingularité de S modulo la relation d’équivalence analytique. La première partie établit l’existence d’une structure non canonique de variété complexe sur ce quotient. La seconde partie se consacre au calcul de sa dimension générique à partir de la donnée d’invariants primitifs topologiques de S. Ce calcul est le fruit de l’étude des valuations des champs de vecteurs tangents à S.

This article proposes to study the moduli space of a germ of curve S in the complex plane, that is to say the equisingularity class of S up to analytical equivalence relation. The first part is devoted to proving that this last quotient can be endowed with a reasonable, yet not canonical, complex structure. The second part deals with the computation of its generic dimension in terms of topological invariants of S. It can be obtained from the study of the valuations of the Saito module of S, Der(logS), i.e. the module of vector fields tangent to S.

Reçu le :
Révisé le :
Accepté le :
Première publication :
DOI : 10.5802/aif.3655
Classification : 32S65, 14H20, 14Q05
Keywords: Complex curves, Foliations, Vector fields, Zariski problem.
Mot clés : Courbes complexes, feuilletages, champs de vecteurs, problem de Zariski.

Genzmer, Yohann 1

1 Institut de Mathématiques de Toulouse, 118, route de Narbonne, 31062 Toulouse Cedex 09 (France) 
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Genzmer, Yohann. The Saito module and the moduli of a germ of curve in $(\mathbb{C}^{2},0)$.. Annales de l'Institut Fourier, Online first, 55 p.

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