Explicit birational geometry of 3-folds of general type, I

Details Explicit birational geometry of 3-folds of general type, I Explicit birational geometry of 3-folds of general type, I

2008-10-28

arxiv.org/abs/0810.5041v2

Mathematics

Algebraic Geometry

29 pages, Ann Sci Ecole Norm Sup (to appear)

Scientific paper

Let $V$ be a complex nonsingular projective 3-fold of general type. We prove $P_{12}(V):=\text{dim} H^0(V, 12K_V)>0$ and $P_{m_0}(V)>1$ for some positive integer $m_0\leq 24$. A direct consequence is the birationality of the pluricanonical map $\varphi_m$ for all $m\geq 126$. Besides, the canonical volume $\text{Vol}(V)$ has a universal lower bound $\nu(3)\geq \frac{1}{63\cdot 126^2}$.

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