Non-embeddable $1$-convex manifolds

Stevens, Jan

Non-embeddable

1

-convex manifolds

Stevens, Jan

Annales de l'Institut Fourier, Volume 64 (2014) no. 5, p. 2205-2222

Abstract
Résumé

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 $c D_{4}$ -singularities.

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 $c D_{4}$ .

MR 3330936 | Zbl 06387336

DOI : https://doi.org/10.5802/aif.2909
Classification: 32S45, 32F10, 32Q15, 32T15, 13C20, 14E30
Keywords: 1-convex manifolds, small resolutions

@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, Volume 64 (2014) no. 5, pp. 2205-2222. doi : 10.5802/aif.2909. http://www.numdam.org/item/AIF_2014__64_5_2205_0/

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