Boundedness of polarized log Calabi-Yau fibrations

Abstract

In this paper, we investigate the boundedness of log pairs with log Calabi--Yau fibration structures. We prove that total spaces of log Calabi--Yau fibrations are bounded modulo crepant birational equivalence when the Iitaka volumes of log canonical divisors are bounded and general fibers are in a bounded family of polarized log Calabi--Yau pairs.