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

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

2008-10-28

arxiv.org/abs/0810.5044v2

Mathematics

Algebraic Geometry

Updated version, Journal of Differential Geometry (to appear)

Scientific paper

Let $V$ be a complex nonsingular projective 3-fold of general type. We shall give a detailed classification up to baskets of singularities on a minimal model of $V$. We show that the $m$-canonical map of $V$ is birational for all $m\geq 73$ and that the canonical volume $\text{Vol}(V)\geq {1/2660}$. When $\chi(\mathcal{O}_V)\leq 1$, our result is $\text{Vol}(V)\geq {1/420}$, which is optimal. Other effective results are also included in the paper.

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