The log minimal model program for Kähler $3$-folds

Abstract

In this article we show that the Log Minimal Model Program for $\mathbb{Q}$-factorial dlt pairs $(X,B)$ on a compact Kähler $3$-fold holds. More specifically, we show that after finitely many divisorial contractions and flips we obtain either a (log) minimal model or a Mori fiber space. We also prove a base point free theorem Kähler $3$-folds.

arXiv commentFinal version. To appear in the Journal of Differential Geometry