Letters of a Bi-Rationalist: VII. Ordered termination

2006/07/31 by Shokurov, V. V. · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0607822

Abstract

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.

Cited by

• Effective termination of general type MMPs in dimension at most five

Related

• Log minimal models according to Shokurov
• Mld's vs thresholds and flips
• On existence of log minimal models II
• ACC for log canonical thresholds and termination of log flips
• The LMMP for log canonical 3-folds in char p