Explicit birational geometry of threefolds of general type, I
[Géométrie birationnelle explicite des variétés de type général de dimension 3, I]
Chen, Jungkai A. ; Chen, Meng
Annales scientifiques de l'École Normale Supérieure, Tome 43 (2010), p. 365-394 / Harvested from Numdam

Soit V une variété non singulière complexe de type général et de dimension 3. Nous montrons P 12 (V):=dimH 0 (V,12K V )>0 et P m 0 (V)>1 pour un certain entier m 0 24. Une conséquence directe est la birationalité de l’application pluricanonique ϕ m pour tout m126. De plus, le volume canonique Vol(V) a un minorant universel ν(3)1 63·126 2 .

Let V be a complex nonsingular projective 3-fold of general type. We prove P 12 (V):=dimH 0 (V,12K V )>0 and P m 0 (V)>1 for some positive integer m 0 24. A direct consequence is the birationality of the pluricanonical map ϕ m for all m126. Besides, the canonical volume Vol(V) has a universal lower bound ν(3)1 63·126 2 .

Publié le : 2010-01-01
DOI : https://doi.org/10.24033/asens.2124
Classification:  14J30,  14B05
Mots 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},
     volume = {43},
     year = {2010},
     pages = {365-394},
     doi = {10.24033/asens.2124},
     mrnumber = {2667020},
     zbl = {1194.14060},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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, Tome 43 (2010) pp. 365-394. doi : 10.24033/asens.2124. http://gdmltest.u-ga.fr/item/ASENS_2010_4_43_3_365_0/

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