Non-embeddable $1$-convex manifolds

Stevens, Jan

Annales de l'Institut Fourier, Tome 64 (2014) no. 5, pp. 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 $c{D}_4$.

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 $c{D}_4$-singularities.

Classification : 32S45, 32F10, 32Q15, 32T15, 13C20, 14E30
Keywords: 1-convex manifolds, small resolutions
Mot clés : variétés 1-convexes, petites résolutions

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