no. 7
Every connected sum of lens spaces is a real component of a uniruled algebraic variety
[Toute somme connexe d'espaces lenticulaires est une composante réelle d'une variété algébrique uniréglée]
Huisman, Johannes1 ; Mangolte, Frédéric2
1 Université de Bretagne Occidentale, Département de Mathématiques, CNRS UMR 6205, 6 avenue Victor Le Gorgeu, CS 93837, 29238 Brest cedex 3 (France)
2 Université de Savoie, Laboratoire de Mathématiques, 73376 Le Bourget du Lac Cedex (France)
Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2475-2487.

Nous montrons qu'une somme connexe finie d'espaces lenticulaires est difféomorphe à une composante réelle d'une variété projective uniréglée et prouvons une conjecture de János Kollár.

We show that any finite connected sum of lens spaces is diffeomorphic to a real component of a uniruled projective variety, and prove a conjecture of János Kollár.

DOI : 10.5802/aif.2167
Classification : 14P25
Keywords: Uniruled algebraic variety, Seifert fibered manifold, lens space, connected sum, equivariant line bundle, real algebraic model, Uniruled algebraic variety, Seifert fibered manifold, lens space, connected sum, equivariant line bundle, real algebraic model
Mot clés : variété uniréglée, variété de Seifert, espace lenticulaire, somme connexe, modèle algébrique réel, fibré en droite équivariant
Huisman, Johannes 1 ; Mangolte, Frédéric 2

1 Université de Bretagne Occidentale, Département de Mathématiques, CNRS UMR 6205, 6 avenue Victor Le Gorgeu, CS 93837, 29238 Brest cedex 3 (France)
2 Université de Savoie, Laboratoire de Mathématiques, 73376 Le Bourget du Lac Cedex (France) 
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Huisman, Johannes; Mangolte, Frédéric. Every connected sum of lens spaces is a real component of a uniruled algebraic variety. Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2475-2487. doi : 10.5802/aif.2167. https://aif.centre-mersenne.org/articles/10.5802/aif.2167/

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