On a conjecture of Hacon and McKernan in dimension three

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 $r\ge r_3$ 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.

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

References in corpus (1)

• Explicit birational geometry of threefolds of general type

Cited by in corpus (2)

• On Effective log Iitaka Fibration for 3-folds and 4-folds
• Effective log Iitaka fibrations for surfaces and threefolds