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.
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] Sulla connessione delle superfizie razionali reali, Annali di Math., Tome 23 (1914), pp. 215-283 | JFM 45.0889.02
[2] Algebraic realization of equivariant vector bundles, J. reine angew. Math., Tome 448 (1994), pp. 31-64 | MR 1266746 | Zbl 0787.57016
[3] 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] Variétés de Fano réelles (d'après C. Viterbo), Séminaire Bourbaki, Tome 872 (1999/2000) | Numdam | Zbl 1004.53059
[5] The Nash conjecture for threefolds, ERA of Amer. Math. Soc., Tome 4 (1998), pp. 63-73 | MR 1641168 | Zbl 0896.14030
[6] Real algebraic threefolds. II. Minimal model program, J. Amer. Math. Soc., Tome 12 (1999), pp. 33-83 | Article | MR 1639616 | Zbl 0964.14013
[7] Real algebraic, J. Math. Sci., New York, Tome 94 (1999), pp. 996-1020 | Article | MR 1703903 | Zbl 0964.14014
[8] The topology of real and complex algebraic varieties, Adv. Stud. Pure Math. (2001) | MR 1865090 | Zbl 1036.14010
[9] On the Kodaira dimension of a minimal threefold, Math. Ann., Tome 281 (1988), pp. 325-332 | Article | MR 949837 | Zbl 0625.14023
[10] 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] Real algebraic manifolds, Ann. Math., Tome 56 (1952), pp. 405-421 | Article | MR 50928 | Zbl 0048.38501
[12] The geometries of 3-manifolds, Bull. London Math. Soc., Tome 15 (1983), pp. 401-487 | Article | MR 705527 | Zbl 0561.57001