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.

arXiv comment17 pages, Introduction reorganized, Remark 3.2 added, Proceedings of the American Mathematical Society (to appear)

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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