Utilisant les résultats de la première et de la deuxième partie de ce travail, nous considérons des variétiés kählériennes minimales de dimension 3, i.e. dont le fibré canonique est nef. Alors est un fibré « good », i.e. dont la dimension de Kodaira est égale à la dimension de Kodaira numérique, sous l’exception possible que est simple, (i.e. il n’existe pas une sous-variété compacte contenant un points très general) et non Kummer. Le deuxième théorème dit que les variétés kählériennes de dimension 3 avec des singularités terminales de sorte que n’est pas nef, ont des contractions de Mori.
Based on the results of the first two parts to this paper, we prove that the canonical bundle of a minimal Kähler threefold (i.e. is nef) is good, i.e. its Kodaira dimension equals the numerical Kodaira dimension, (in particular some multiple of is generated by global sections); unless is simple. “Simple“ means that there is no compact subvariety through the very general point of and not Kummer. Moreover we show that a compact Kähler threefold with only terminal singularities whose canonical bundle is not nef, admits a contraction unless is simple with Kodaira dimension
@article{BSMF_2001__129_3_339_0, author = {Peternell, Thomas}, title = {Towards a Mori theory on compact K\"ahler~threefolds III}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, volume = {129}, year = {2001}, pages = {339-356}, doi = {10.24033/bsmf.2400}, mrnumber = {1881199}, zbl = {0994.32017}, language = {en}, url = {http://dml.mathdoc.fr/item/BSMF_2001__129_3_339_0} }
Peternell, Thomas. Towards a Mori theory on compact Kähler threefolds III. Bulletin de la Société Mathématique de France, Tome 129 (2001) pp. 339-356. doi : 10.24033/bsmf.2400. http://gdmltest.u-ga.fr/item/BSMF_2001__129_3_339_0/
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