Formal classification of two-dimensional neighborhoods of genus g≥2 curves with trivial normal bundle  [ Classification formelle des voisinages de courbes de genre g≥2 avec fibré normal trivial ]
Annales de l'Institut Fourier, à paraître, 22 p.

On étudie dans ce papier la classification formelle des voisinages de dimension deux de courbes de genre g≥2 dont le fibré normal est trivial. On construit tout d’abord sur de tels voisinages des feuilletages formels dont l’holonomie s’annule le long de nombreux lacets, puis on donne la classification formelle / analytique des voisinages équipés de deux feuilletages, et finalement on rassemble tout cela pour obtenir une description de l’espace des voisinages modulo équivalence formelle.

In this paper we study the formal classification of two-dimensional neighborhoods of genus g≥2 curves with trivial normal bundle. We first construct formal foliations on such neighborhoods with holonomy vanishing along many loops, then give the formal / analytic classification of neighborhoods equipped with two foliations, and finally put this together to obtain a description of the space of neighborhoods up to formal equivalence.

Reçu le : 2018-07-09
Révisé le : 2019-04-02
Accepté le : 2019-07-11
Première publication : 2020-10-01
Classification : 32Q57,  32G12,  37F75
Mots clés: voisinages formels, feuilletages 
@unpublished{AIF_0__0_0_A16_0,
     author = {Thom, Olivier},
     title = {Formal classification of two-dimensional neighborhoods of genus $g\ge 2$ curves with trivial normal bundle},
     note = {to appear in \emph{Annales de l'Institut Fourier}},
}
Thom, Olivier. Formal classification of two-dimensional neighborhoods of genus $g\ge 2$ curves with trivial normal bundle. Annales de l'Institut Fourier, à paraître, 22 p.

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