Existence of the equivariant minimal model program for compact Kähler threefolds with the action of an abelian group of maximal rank

Abstract

Let X be a Q-factorial compact Kähler 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 [Zho22, Theorem 1.3].