Letters of a Bi-Rationalist: VII. Ordered termination

Details Letters of a Bi-Rationalist: VII. Ordered termination Letters of a Bi-Rationalist: VII. Ordered termination

2006-07-31

arxiv.org/abs/math/0607822v2

Mathematics

Algebraic Geometry

Scientific paper

To construct a resulting model in LMMP is sufficient to prove existence of log flips and their termination for certain sequences. We prove that LMMP in dimension $d-1$ and termination of terminal log flips in dimension $d$ imply, for any log pair of dimension $d$, the existence of a {\em resulting} log model: a strictly log minimal model or a strictly log terminal Mori log fibration, and imply existence of log flips in dimension $d+1$. As consequence, we prove existence of a resulting model of 4-fold log pairs, existence of log flips in dimension 5, and some fragments of Geography of log models in dimension 4.

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