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) 
@article{AIF_2005__55_7_2475_0,
     author = {Huisman, Johannes and Mangolte, Fr\'ed\'eric},
     title = {Every connected sum of lens spaces is a real component of a uniruled algebraic variety},
     journal = {Annales de l'Institut Fourier},
     pages = {2475--2487},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {55},
     number = {7},
     year = {2005},
     doi = {10.5802/aif.2167},
     mrnumber = {2207390},
     zbl = {1092.14070},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.2167/}
}
TY  - JOUR
AU  - Huisman, Johannes
AU  - Mangolte, Frédéric
TI  - Every connected sum of lens spaces is a real component of a uniruled algebraic variety
JO  - Annales de l'Institut Fourier
PY  - 2005
SP  - 2475
EP  - 2487
VL  - 55
IS  - 7
PB  - Association des Annales de l’institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.2167/
DO  - 10.5802/aif.2167
LA  - en
ID  - AIF_2005__55_7_2475_0
ER  - 
%0 Journal Article
%A Huisman, Johannes
%A Mangolte, Frédéric
%T Every connected sum of lens spaces is a real component of a uniruled algebraic variety
%J Annales de l'Institut Fourier
%D 2005
%P 2475-2487
%V 55
%N 7
%I Association des Annales de l’institut Fourier
%U http://archive.numdam.org/articles/10.5802/aif.2167/
%R 10.5802/aif.2167
%G en
%F AIF_2005__55_7_2475_0
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. http://archive.numdam.org/articles/10.5802/aif.2167/

[1] Comessatti, A. Sulla connessione delle superfizie razionali reali, Annali di Math., Volume 23 (1914), pp. 215-283 | JFM

[2] Dovermann, K.H.; Masuda, M.; Suh, D.Y. Algebraic realization of equivariant vector bundles, J. reine angew. Math., Volume 448 (1994), pp. 31-64 | MR | Zbl

[3] Huisman, J.; Mangolte, F. Every orientable Seifert 3-manifold is a real component of a uniruled algebraic variety, Topology, Volume 44 (2005), pp. 63-71 | DOI | MR | Zbl

[4] Kharlamov, V. Variétés de Fano réelles (d'après C. Viterbo), Séminaire Bourbaki, Volume 872 (1999/2000) | Numdam | Zbl

[5] Kollár, J. The Nash conjecture for threefolds, ERA of Amer. Math. Soc., Volume 4 (1998), pp. 63-73 | MR | Zbl

[6] Kollár, J. Real algebraic threefolds. II. Minimal model program, J. Amer. Math. Soc., Volume 12 (1999), pp. 33-83 | DOI | MR | Zbl

[7] Kollár, J. Real algebraic, J. Math. Sci., New York, Volume 94 (1999), pp. 996-1020 | DOI | MR | Zbl

[8] Kollár, J. The topology of real and complex algebraic varieties, Adv. Stud. Pure Math. (2001) | MR | Zbl

[9] Miyaoka, Y. On the Kodaira dimension of a minimal threefold, Math. Ann., Volume 281 (1988), pp. 325-332 | DOI | MR | Zbl

[10] Mori, S. Flip theorem and the existence of minimal models for threefolds, J. Amer. Math. Soc., Volume 1 (1988), pp. 117-253 | MR | Zbl

[11] Nash, J. Real algebraic manifolds, Ann. Math., Volume 56 (1952), pp. 405-421 | DOI | MR | Zbl

[12] Scott, P. The geometries of 3-manifolds, Bull. London Math. Soc., Volume 15 (1983), pp. 401-487 | DOI | MR | Zbl

Cité par Sources :