Existence of the equivariant minimal model program for compact K\"ahler threefolds with the action of an abelian group of maximal rank

Abstract

Let $X$ be a $\mathbb{Q}$-factorial compact K\"ahler klt threefold admitting an action of a free abelian group $G$, which is of positive entropy and of maximal rank. After running the $G$-equivariant log minimal model program, we show that such $X$ is either rationally connected or bimeromorphic to a $Q$-complex torus. In particular, we fix an issue in the proof of our previous paper.