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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.

##### MSC:
 14C20 Divisors, linear systems, invertible sheaves
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