Non-embeddable 1-convex manifolds
Annales de l'Institut Fourier, Volume 64 (2014) no. 5, pp. 2205-2222.

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.

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 .

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

1 Matematiska vetenskaper Göteborgs universitet och Chalmers tekniska högskola 41296 Göteborg (Sweden)
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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/articles/10.5802/aif.2909/

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