Effective log Iitaka fibrations for surfaces and threefolds

Abstract

We prove an analogue of Fujino and Mori's ``bounding the denominators'' in the log canonical bundle formula (see also Prokhorov and Shokurov) for Kawamata log terminal pairs of relative dimension one. As an application we prove that for a klt pair $(X,\Delta )$ of Kodaira codimension one and dimension at most three such that the coefficients of $\Delta$ are in a DCC set $\mathcal{A}$, there is a natural number $N$ that depends only on $\mathcal{A}$ for which the round down of $\mathbb{N}(K_X+\Delta )$ induces the Iitaka fibration. We also prove a birational boundedness result for klt surfaces of general type.

References in corpus (1)

• On a conjecture of Hacon and McKernan in dimension three

Cited by in corpus (1)

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