2023/01/12 by Guodu Chen, Jingjun Han, Chen, Guodu +3
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.2301.04813
We study the relationship between Iitaka fibrations and the conjecture on the existence of complements, assuming the good minimal model conjecture. In one direction, we show that the conjecture on the existence of complements implies the effective log Iitaka fibration conjecture. As a consequence, the effective log Iitaka fibration conjecture holds in dimension 3. In the other direction, for any Calabi-Yau type variety X such that -KX is nef, we show that X has an n-complement for some universal constant n depending only on the dimension of X and two natural invariants of a general fiber of an Iitaka fibration of -KX. We also formulate the decomposable Iitaka fibration conjecture, a variation of the effective log Iitaka fibration conjecture which is closely related to the structure of ample models of pairs with non-rational coefficients, and study its relationship with the forestated conjectures.