Log minimal models according to Shokurov

TL;DR

This paper provides a concise proof that in dimension 4, any klt pair has a log minimal model or a Mori fiber space, based on Shokurov's ideas and the termination of terminal log flips.

Contribution

It offers a simplified proof of the existence of log minimal models for klt pairs in dimension 4, extending Shokurov's results.

Findings

Proof that termination of terminal log flips implies existence of log minimal models in dimension 4

Establishment of log minimal models or Mori fiber spaces for klt pairs in dimension 4

Simplified proof based on Shokurov's ideas

Abstract

Following Shokurov's ideas, we give a short proof of the following klt version of his result: termination of terminal log flips in dimension d implies that any klt pair of dimension d has a log minimal model or a Mori fibre space. Thus, in particular, any klt pair of dimension 4 has a log minimal model or a Mori fibre space.