# On existence of log minimal models II

@inproceedings{Birkar2011OnEO,
title={On existence of log minimal models II},
author={C. Birkar},
year={2011}
}
Abstract We prove that the existence of log minimal models in dimension d essentially implies the LMMP with scaling in dimension d. As a consequence we prove that a weak nonvanishing conjecture in dimension d implies the minimal model conjecture in dimension d.
On the non-vanishing conjecture and existence of log minimal models
We prove that the non-vanishing conjecture and the log minimal model conjecture for projective log canonical pairs can be reduced to the non-vanishing conjecture for smooth projective varieties suchExpand
On existence of log minimal models
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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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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.
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We prove a stronger version of a termination theorem appeared in the paper "On existence of log minimal models II". We essentially just get rid of the redundant assumptions so the proof is almost theExpand
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Abstract Under the assumption of the minimal model theory for projective klt pairs of dimension n, we establish the minimal model theory for lc pairs ( X / Z , Δ ) {(X/Z,\Delta)} such that the logExpand
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#### References

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