Explicit birational geometry of threefolds of general type, I
[Géométrie birationnelle explicite des variétés de type général de dimension 3, I]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 43 (2010) no. 3, pp. 365-394.

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 .

DOI : 10.24033/asens.2124
Classification : 14J30, 14B05
Keywords: 3-folds, plurigenus
Mot clés : variétés de dimension 3, plurigenre
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Chen, Jungkai A.; Chen, Meng. Explicit birational geometry of threefolds of general type, I. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 43 (2010) no. 3, pp. 365-394. doi : 10.24033/asens.2124. http://archive.numdam.org/articles/10.24033/asens.2124/

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