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arXiv · 0708.3662

On a conjecture of Hacon and McKernan in dimension three

Adam Ringler
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Abstract

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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Adam Ringler. 2007-09-13. On a conjecture of Hacon and McKernan in dimension three. https://arxiv.org/abs/0708.3662

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