Some remarks on the minimal model program for log canonical pairs

Abstract

We prove that the target space of an extremal Fano contraction from a log canonical pair has only log canonical singularities. We also treat some related topics, for example, the finite generation of canonical rings for compact Kähler manifolds, and so on. The main ingredient of this paper is the nefness of the moduli parts of lc-trivial fibrations. We also give some observations on the semi-ampleness of the moduli parts of lc-trivial fibrations. For the reader's convenience, we discuss some examples of non-Kähler manifolds, flopping contractions, and so on, in order to clarify our results.

37 pages, v2: title changed, major revision, v3: update the reference list, v4: Section 6 on non-Kähler manifolds is new, v5: minor revision following referee's comment, v6: References were updated, final version, to appear in Kodaira Centennial issue of the Journal of Mathematical Sciences, the University of Tokyo

References in corpus (4)

• Introduction to the log minimal model program for log canonical pairs
• Log pluricanonical representations and abundance conjecture
• Higher direct images of log canonical divisors and positivity theorems
• Notes on the weak positivity theorems

Cited by in corpus (8)

• Quotients of higher dimensional Cremona groups
• On semipositivity, injectivity and vanishing theorems
• On normalization of quasi-log canonical pairs
• Fundamental properties of basic slc-trivial fibrations, II
• Building blocks of polarized endomorphisms of normal projective varieties
• Minimal model theory for relatively trivial log canonical pairs
• Normal projective varieties admitting polarized or int-amplified endomorphisms
• The K"ahler-Ricci flow with Log Canonical Singularities