[Toute somme connexe d'espaces lenticulaires est une composante réelle d'une variété algébrique uniréglée]
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.
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
@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://www.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://www.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://www.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://www.numdam.org/articles/10.5802/aif.2167/
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