[Variétés 1-convexes non plongeables]
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 . À cette fin, nous étudions de petites résolutions des singularités .
We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable -convex manifold.
We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type . To this end we study small resolutions of -singularities.
Keywords: 1-convex manifolds, small resolutions
Mot clés : variétés 1-convexes, petites résolutions
Stevens, Jan 1
@article{AIF_2014__64_5_2205_0,
author = {Stevens, Jan},
title = {Non-embeddable $1$-convex manifolds},
journal = {Annales de l'Institut Fourier},
pages = {2205--2222},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {64},
number = {5},
year = {2014},
doi = {10.5802/aif.2909},
mrnumber = {3330936},
zbl = {06387336},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2909/}
}
TY - JOUR AU - Stevens, Jan TI - Non-embeddable $1$-convex manifolds JO - Annales de l'Institut Fourier PY - 2014 SP - 2205 EP - 2222 VL - 64 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2909/ DO - 10.5802/aif.2909 LA - en ID - AIF_2014__64_5_2205_0 ER -
%0 Journal Article %A Stevens, Jan %T Non-embeddable $1$-convex manifolds %J Annales de l'Institut Fourier %D 2014 %P 2205-2222 %V 64 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2909/ %R 10.5802/aif.2909 %G en %F 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://aif.centre-mersenne.org/articles/10.5802/aif.2909/
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