Minimal model theory for relatively trivial log canonical pairs

We study relative log canonical pairs with relatively trivial log canonical divisors. We fix such a pair $(X,\Delta)/Z$ and establish the minimal model theory for the pair $(X,\Delta)$ assuming the minimal model theory for all Kawamata log terminal pairs whose dimension is not greater than ${\rm dim}\,Z$. We also show the finite generation of log canonical rings for log canonical pairs of dimension five which are not of log general type.Comment: 38 pages, final version. The statement of Theorem 1.2 was replaced by that of Theorem 4.2, which was equivalent to Theorem 1.2. Accompanied by this, Lemma 4.1 and Theorem 4.2 was removed. Numbering of definitions and others in Section 2 and Section 4 was changed. Other minor changes. To appear in Ann. Inst. Fourier (Grenoble

ADJUNCTION AND INVERSION OF ADJUNCTION

We establish adjunction and inversion of adjunction for log canonical centers of arbitrary codimension in full generality