Compact Kähler threefolds with the action of an abelian group of maximal rank
Copyright policy )Compact Kähler threefolds with the action of an abelian group of maximal rank
In this note, we study the normal compact K��hler (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-��tale quotient of a complex $3$-torus.
17 pages, Introduction reorganized, Remark 3.2 added, Proceedings of the American Mathematical Society (to appear)
- National University of Singapore Singapore
automorphisms, Dynamical Systems (math.DS), Abelian varieties of dimension \(> 1\), Mathematics - Algebraic Geometry, tori, 08A35, 14J50, 11G10, Automorphisms of surfaces and higher-dimensional varieties, FOS: Mathematics, Mathematics - Dynamical Systems, compact Kähler threefolds, complex dynamics, Algebraic Geometry (math.AG)
automorphisms, Dynamical Systems (math.DS), Abelian varieties of dimension \(> 1\), Mathematics - Algebraic Geometry, tori, 08A35, 14J50, 11G10, Automorphisms of surfaces and higher-dimensional varieties, FOS: Mathematics, Mathematics - Dynamical Systems, compact Kähler threefolds, complex dynamics, Algebraic Geometry (math.AG)
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