Corpus ID: 115176712

Introduction to the log minimal model program for log canonical pairs

@article{Fujino2009IntroductionTT,
  title={Introduction to the log minimal model program for log canonical pairs},
  author={O. Fujino},
  journal={arXiv: Algebraic Geometry},
  year={2009}
}
  • O. Fujino
  • Published 2009
  • Mathematics
  • arXiv: Algebraic Geometry
We describe the foundation of the log minimal model program for log canonical pairs according to Ambro's idea. We generalize Koll\'ar's vanishing and torsion-free theorems for embedded simple normal crossing pairs. Then we prove the cone and contraction theorems for quasi-log varieties, especially, for log canonical pairs. 
INTRODUCTION TO THE THEORY OF QUASI-LOG VARIETIES
This paper is a gentle introduction to the theory of quasi-log varieties by Ambro. We explain the fundamental theo- rems for the log minimal model program for log canonical pairs. More precisely, weExpand
NON-VANISHING THEOREM FOR LOG CANONICAL PAIRS
We obtain a correct generalization of Shokurov's non- vanishing theorem for log canonical pairs. It implies the base point free theorem for log canonical pairs. We also prove the rationality theoremExpand
Kodaira vanishing theorem for log-canonical and semi-log-canonical pairs
We prove the Kodaira vanishing theorem for log-canonical and semi-log-canonical pairs. We also give a relative vanishing theorem of Reid--Fukuda type for semi-log-canonical pairs.
Fundamental theorems for semi log canonical pairs
We prove that every quasi-projective semi log canonical pair has a quasi-log structure with several good properties. It implies that various vanishing theorems, torsion-free theorem, and the cone andExpand
EFFECTIVE BASE POINT FREE THEOREM FOR LOG CANONICAL PAIRS—KOLLÁR TYPE THEOREM
Kollar's effective base point free theorem for kawamata log terminal pairs is very important and was used in Hacon-McKernan's proof of pl flips. In this paper, we generalize Kollar's theorem for logExpand
Some Remarks on the Minimal Model Program for Log Canonical Pairs
We prove that the target space of an extremal Fano contraction from a log canonical pair has only log canonical singu- larities. We also treat some related topics, for example, the finite generationExpand
Some remarks on the minimal model program
We prove that the target space of an extremal Fano contraction from a log canonical pair has only log canonical singularities. We also treat some related topics, for example, the finite generation ofExpand
Fundamental Theorems for the Log Minimal Model Program
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.
FUNDAMENTAL THEOREMS FOR THE LOG MINIMAL MODEL PROGRAM
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.
EFFECTIVE BASE POINT FREE THEOREM FOR LOG CANONICAL PAIRS
Kollár’s effective base point free theorem for kawamata log terminal pairs is very important and was used in Hacon– McKernan’s proof of pl flips. In this paper, we generalize Kollár’s theorem for logExpand
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References

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We obtain a correct generalization of Shokurov's non- vanishing theorem for log canonical pairs. It implies the base point free theorem for log canonical pairs. We also prove the rationality theoremExpand
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Kollar's effective base point free theorem for kawamata log terminal pairs is very important and was used in Hacon-McKernan's proof of pl flips. In this paper, we generalize Kollar's theorem for logExpand
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We explain the fundamental theorems for the log min- imal model program for log canonical pairs.
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  • Mathematics
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Abstract In this paper, we prove that the log minimal model program in dimension d−1 implies the existence of log minimal models for effective lc pairs (e.g. of non-negative Kodaira dimension) inExpand
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