On a conjecture of Hacon and McKernan in dimension three

Details On a conjecture of Hacon and McKernan in dimension three On a conjecture of Hacon and McKernan in dimension three

2007-08-27

arxiv.org/abs/0708.3662v2

Mathematics

Algebraic Geometry

13 pages; Lemma 3.4 and 3.5 corrected; Other minor corrections fixed

Scientific paper

We prove that there exists a universal constant $r_3$ such that if $X$ is a smooth projective threefold over $\mathbb{C}$ with non-negative Kodaira dimension, then the linear system $|r K_X|$ admits a fibration that is birational to the Iitaka fibration as soon as $r \geq r_3$ and sufficiently divisible. This gives an affirmative answer to a conjecture of Hacon and McKernan in the case of threefolds. Viehweg and Zhang have posted a stronger result along these lines using different methods.

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