Uniform log Iitaka fibrations and bounded moduli denominators

Abstract — v1

For normal projective log canonical pairs over algebraically closed fields of characteristic zero, of fixed dimension d ≥ 5 and with effective boundary coefficients in a fixed finite rational set, we prove that one complete rounded pluricanonical system generates the full Iitaka field whenever the ℚ-Cartier log canonical divisor has nonnegative Kodaira dimension. Its degree depends only on the dimension and coefficient set. For the paper's normalized canonical bundle formulae over ℂ, we also bound the Cartier denominators of the moduli divisors on smooth projective determining models in terms of the dimension and coefficient set.