Every connected sum of lens spaces is a real component of a uniruled algebraic variety
Annales de l'Institut Fourier, Volume 55 (2005) no. 7, p. 2475-2487

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.

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.

DOI : https://doi.org/10.5802/aif.2167
Classification:  14P25
Keywords: Uniruled algebraic variety, Seifert fibered manifold, lens space, connected sum, equivariant line bundle, real algebraic model
Keywords: Uniruled algebraic variety, Seifert fibered manifold, lens space, connected sum, equivariant line bundle, real algebraic model 
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {7},
     year = {2005},
     pages = {2475-2487},
     doi = {10.5802/aif.2167},
     zbl = {1092.14070},
     mrnumber = {2207390},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 55 (2005) no. 7, pp. 2475-2487. doi : 10.5802/aif.2167. http://www.numdam.org/item/AIF_2005__55_7_2475_0/

[1] Comessatti, A. Sulla connessione delle superfizie razionali reali, Annali di Math., Tome 23 (1914), pp. 215-283 | JFM 45.0889.02

[2] Dovermann, K.H.; Masuda, M.; Suh, D.Y. Algebraic realization of equivariant vector bundles, J. reine angew. Math., Tome 448 (1994), pp. 31-64 | MR 1266746 | Zbl 0787.57016

[3] Huisman, J.; Mangolte, F. Every orientable Seifert 3-manifold is a real component of a uniruled algebraic variety, Topology, Tome 44 (2005), pp. 63-71 | Article | MR 2104001 | Zbl 02137339

[4] Kharlamov, V. Variétés de Fano réelles (d'après C. Viterbo), Séminaire Bourbaki, Tome 872 (1999/2000) | Numdam | Zbl 1004.53059

[5] Kollár, J. The Nash conjecture for threefolds, ERA of Amer. Math. Soc., Tome 4 (1998), pp. 63-73 | MR 1641168 | Zbl 0896.14030

[6] Kollár, J. Real algebraic threefolds. II. Minimal model program, J. Amer. Math. Soc., Tome 12 (1999), pp. 33-83 | Article | MR 1639616 | Zbl 0964.14013

[7] Kollár, J. Real algebraic, J. Math. Sci., New York, Tome 94 (1999), pp. 996-1020 | Article | MR 1703903 | Zbl 0964.14014

[8] Kollár, J. The topology of real and complex algebraic varieties, Adv. Stud. Pure Math. (2001) | MR 1865090 | Zbl 1036.14010

[9] Miyaoka, Y. On the Kodaira dimension of a minimal threefold, Math. Ann., Tome 281 (1988), pp. 325-332 | Article | MR 949837 | Zbl 0625.14023

[10] Mori, S. Flip theorem and the existence of minimal models for threefolds, J. Amer. Math. Soc., Tome 1 (1988), pp. 117-253 | MR 924704 | Zbl 0649.14023

[11] Nash, J. Real algebraic manifolds, Ann. Math., Tome 56 (1952), pp. 405-421 | Article | MR 50928 | Zbl 0048.38501

[12] Scott, P. The geometries of 3-manifolds, Bull. London Math. Soc., Tome 15 (1983), pp. 401-487 | Article | MR 705527 | Zbl 0561.57001