Abundance theorem for semi log canonical threefolds
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In this paper, the abundance theorem for slc three-folds has been proved for B-pluricanonical representations, and it is shown that the abundance of three-fold representations can be reduced to 2.0.Abstract:
0. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 1. Definitions and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 2. Reduced boundaries of dlt n-folds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517 3. Finiteness of B-pluricanonical representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520 4. The abundance theorem for slc threefolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530read more
Citations
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Journal ArticleDOI
Fundamental Theorems for the Log Minimal Model Program
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.
Journal ArticleDOI
Log canonical singularities are Du Bois
János Kollár,Sándor J. Kovács +1 more
TL;DR: In this article, it was shown that log canonical singularities are Du Bois, as conjectured in [Kol92, 1.13] and [1.10].
Journal ArticleDOI
Towards the second main theorem on complements
TL;DR: In this article, the boundedness of complements modulo two conjectures, Borisov-Alexeev conjecture and effective adjunction for fibre spaces, was proved and proved in two particular cases.
Journal ArticleDOI
Existence of log canonical closures
Christopher D. Hacon,Chenyang Xu +1 more
TL;DR: In this article, it was shown that the moduli functor of stable schemes satisfies the valuative criterion for properness, and the existence of log canonical compactifications for open log canonical pairs.
Journal ArticleDOI
Log canonical singularities are Du Bois
János Kollár,Sándor J. Kovács +1 more
TL;DR: In this article, it was shown that log canonical singularities are Du Bois fibers and flatness of the cohomology sheaves of the relative dualizing complex of a projective family with DuBois fibers.
References
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Introduction to the Minimal Model Problem
Book
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TL;DR: The classification of algebraic surfaces is an intricate and fascinating branch of mathematics as mentioned in this paper, and it is an active area of research in the field of geology, which is the subject of this paper.
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