# Supplement to the paper "On existence of log minimal models II"

@article{Birkar2011SupplementTT, title={Supplement to the paper "On existence of log minimal models II"}, author={C. Birkar}, journal={arXiv: Algebraic Geometry}, year={2011} }

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 the same as in there. However, we give a detailed proof here for future reference.

#### One Citation

Existence of log canonical flips and a special LMMP

- Mathematics
- 2011

Let (X/Z,B+A) be a Q-factorial dlt pair where B,A≥0 are Q-divisors and KX+B+A∼Q0/Z. We prove that any LMMP/Z on KX+B with scaling of an ample/Z divisor terminates with a good log minimal model or a… Expand

#### References

SHOWING 1-7 OF 7 REFERENCES

On existence of log minimal models II

- Mathematics
- 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… Expand

Fundamental Theorems for the Log Minimal Model Program

- Mathematics
- 2009

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.

On existence of log minimal models

- Mathematics
- Compositio Mathematica
- 2010

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) in… Expand

Existence of minimal models for varieties of log general type

- Mathematics
- 2006

Assuming finite generation in dimension n − 1, we prove that pl-flips exist in dimension n.

Quasi-log varieties

- Mathematics
- 2001

We extend the Cone Theorem of the Log Minimal Model Program to log varieties with arbitrary singularities.

Quasi - log varieties . Tr . Mat . Inst . Steklova 240 ( 2003 ) , Biratsion . Geom . Linein . Sist . Konechno Porozhden - nye Algebry , 220 - 239 ; translation in

- Proc . Steklov Inst . Math .
- 2003

3-fold log flips. With an appendix in English by Yujiro Kawamata

- Russian Acad. Sci. Izv. Math
- 1993