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Subadjunction of log canonical divisors. II. (English) Zbl 0919.14003
[For part I of this paper see: Y. Kawamata in: Birational algebraic geometry, Conf. Algebr. Geom. Memory W. Chow, Baltimore 1996, Contemp. Math. 207, 79-88 (1997; Zbl 0901.14004).]
A subadjunction theorem for codimension \(2\) subvarieties of a normal variety has been proved by the author in part I (loc. cit.). Here a subadjunction theorem is given for subvarieties of arbitrary codimension of a normal variety \(X\), with two fixed effective \(\mathbb Q\)-divisors \(D^{\circ}\) and \(D\), such that \(D^\circ< D\), \((X,D^\circ)\) is log terminal and \((X,D)\) is log canonical. In this situation, there exists a minimal element among the centres of log canonical singularities for \((X,D)\) with respect to the inclusions. Such a minimal centre \(W\) is always normal. The theorem says that, if \(H\) is an ample Cartier divisor on \(X\) and \(\varepsilon\) is any positive rational number, then there exists an effective \(\mathbb Q\)-divisor \(D_W\) on \(W\) such that \((K_X+D+\varepsilon H)\mid_W\sim_{\mathbb Q} K_W+D_W\) and that the pair \((W, D_W)\) is log terminal.

14C20 Divisors, linear systems, invertible sheaves
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