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Explicit birational geometry of threefolds of general type, I

Jungkai A. ChenMeng Chen — 2010

Annales scientifiques de l'École Normale Supérieure

Let V be a complex nonsingular projective 3-fold of general type. We prove P 12 ( V ) : = dim H 0 ( V , 12 K 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 m 126 . Besides, the canonical volume Vol ( V ) has a universal lower bound ν ( 3 ) 1 63 · 126 2 .

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