Compact Kähler threefolds with the action of an abelian group of maximal rank

Abstract

In this note, we study the normal compact Kähler (possibly singular) threefold $X$ admitting the action of a free abelian group $G$ of maximal rank, all the non-trivial elements of which are of positive entropy. If such $X$ is further assumed to have only terminal singularities, then we prove that it is either a rationally connected projective threefold or bimeromorphic to a quasi-étale quotient of a complex $3$-torus.

17 pages, Introduction reorganized, Remark 3.2 added, Proceedings of the American Mathematical Society (to appear)

References in corpus (3)

• Some aspects of explicit birational geometry inspired by complex dynamics
• Free abelian group actions on normal projective varieties: sub-maximal dynamical rank case
• Int-amplified endomorphisms of compact Kähler spaces

Cited by in corpus (1)

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