Let be a complex nonsingular projective 3-fold of general type. We prove and for some positive integer . A direct consequence is the birationality of the pluricanonical map for all . Besides, the canonical volume has a universal lower bound .
Soit une variété non singulière complexe de type général et de dimension 3. Nous montrons et pour un certain entier . Une conséquence directe est la birationalité de l’application pluricanonique pour tout . De plus, le volume canonique a un minorant universel .
Keywords: 3-folds, plurigenus
Mot clés : variétés de dimension 3, plurigenre
@article{ASENS_2010_4_43_3_365_0, author = {Chen, Jungkai A. and Chen, Meng}, title = {Explicit birational geometry of threefolds of general type, {I}}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {365--394}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 43}, number = {3}, year = {2010}, doi = {10.24033/asens.2124}, mrnumber = {2667020}, zbl = {1194.14060}, language = {en}, url = {http://www.numdam.org/articles/10.24033/asens.2124/} }
TY - JOUR AU - Chen, Jungkai A. AU - Chen, Meng TI - Explicit birational geometry of threefolds of general type, I JO - Annales scientifiques de l'École Normale Supérieure PY - 2010 SP - 365 EP - 394 VL - 43 IS - 3 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/asens.2124/ DO - 10.24033/asens.2124 LA - en ID - ASENS_2010_4_43_3_365_0 ER -
%0 Journal Article %A Chen, Jungkai A. %A Chen, Meng %T Explicit birational geometry of threefolds of general type, I %J Annales scientifiques de l'École Normale Supérieure %D 2010 %P 365-394 %V 43 %N 3 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/asens.2124/ %R 10.24033/asens.2124 %G en %F ASENS_2010_4_43_3_365_0
Chen, Jungkai A.; Chen, Meng. Explicit birational geometry of threefolds of general type, I. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 43 (2010) no. 3, pp. 365-394. doi : 10.24033/asens.2124. http://www.numdam.org/articles/10.24033/asens.2124/
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