Non-embeddable 1-convex manifolds  [ Variétés 1-convexes non plongeables ]
Annales de l'Institut Fourier, Tome 64 (2014) no. 5, p. 2205-2222
Nous montrons que chaque petite résolution d’une singularité de hypersurface 3-dimensionnelle terminale peut se produire sur une variété 1-convexe non plongeable.Nous donnons un exemple explicite d’une variété non plongeable contenant une courbe exceptionnelle rationnelle irréductible avec fibré normal du type (1,-3). À cette fin, nous étudions de petites résolutions des singularités cD 4 .
We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable 1-convex manifold.We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type (1,-3). To this end we study small resolutions of cD 4 -singularities.
DOI : https://doi.org/10.5802/aif.2909
Classification:  32S45,  32F10,  32Q15,  32T15,  13C20,  14E30
Mots clés: variétés 1-convexes, petites résolutions
@article{AIF_2014__64_5_2205_0,
     author = {Stevens, Jan},
     title = {Non-embeddable $1$-convex manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {5},
     year = {2014},
     pages = {2205-2222},
     doi = {10.5802/aif.2909},
     mrnumber = {3330936},
     zbl = {06387336},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_5_2205_0}
}
Stevens, Jan. Non-embeddable $1$-convex manifolds. Annales de l'Institut Fourier, Tome 64 (2014) no. 5, pp. 2205-2222. doi : 10.5802/aif.2909. https://www.numdam.org/item/AIF_2014__64_5_2205_0/

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