Some Remarks on the Minimal Model Program for Log Canonical Pairs
Vol. 22 (2015), No. 1, Page 149–192.
Fujino, Osamu
Some Remarks on the Minimal Model Program for Log Canonical Pairs
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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.
Keywords: Extremal contractions, Fano contractions, lc-trivial fibrations, canonical bundle formulas, log canonical singularities, compact Kähler manifolds, non-Kähler manifolds.
Mathematics Subject Classification (2010): Primary 14E30; Secondary 14N30, 32J27.
Mathematical Reviews Number: MR3329193
Received: 2013-10-17
