Log abundance of the moduli b-divisors of lc-trivial fibrations

Abstract

We prove that the moduli b-divisor of an lc-trivial fibration from a log canonical pair is log abundant. The result follows from a theorem on the restriction of the moduli b-divisor, based on a theory of lc-trivial morphisms, which allows us to treat $\mathbb{R}$-divisors and proper morphisms possibly with disconnected fibres. We also prove a theorem on extending a finite cover over a closed subvariety to that over a variety in arbitrary characteristic.

44 pages. Re-organized and arguments are simplified. More details added in the proof of Theorem 3.10

Cited by in corpus (3)

• Shokurov's conjecture on conic bundles with canonical singularities
• Iitaka fibrations for dlt pairs polarized by a nef and log big divisor
• An abundance theorem for generalised pairs