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Some remarks on the minimal model program for log canonical pairs. (English) Zbl 1435.14017

Summary: 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.

MSC:

14E30 Minimal model program (Mori theory, extremal rays)
14N30 Adjunction problems
32J27 Compact Kähler manifolds: generalizations, classification
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