2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137796We 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.13 pages; Lemma 3.4 and 3.5 corrected; Other minor corrections fixedAlgebraic Geometrytext