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On quasi-log schemes
TL;DR: In this paper, the authors established the basepoint-free theorem of Reid-Fukuda type for quasi-log schemes in full generality, which means that all the results for quasilog schemes claimed in Ambro's paper hold true.
Abstract: The notion of quasi-log schemes was first introduced by Florin Ambro in his epoch-making paper: Quasi-log varieties. In this paper, we establish the basepoint-free theorem of Reid--Fukuda type for quasi-log schemes in full generality. Roughly speaking, it means that all the results for quasi-log schemes claimed in Ambro's paper hold true. The proof is Kawamata's X-method with the aid of the theory of basic slc-trivial fibrations. For the reader's convenience, we make many comments on the theory of quasi-log schemes in order to make it more accessible.
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648 citations
01 Jan 1987
564 citations
TL;DR: In this article, the authors proved the cone theorem and the contraction theorem for pairs (X;B), where X is a normal variety and B is an effective R-Divisor on X such that KX + B is R-Cartier.
Abstract: In this paper, we prove the cone theorem and the contraction theorem for pairs (X;B), where X is a normal variety and B is an effective R-divisor on X such that KX +B is R-Cartier.
243 citations