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Free abelian group actions on normal projective varieties: submaximal dynamical rank case
Part of:
Surfaces and higher-dimensional varieties
Complex spaces with a group of automorphisms
Topological dynamics
Automorphic functions
Holomorphic mappings and correspondences
Published online by Cambridge University Press: 14 May 2020
Abstract
Let X be a normal projective variety of dimension n and G an abelian group of automorphisms such that all elements of $G\setminus \{\operatorname {id}\}$ are of positive entropy. Dinh and Sibony showed that G is actually free abelian of rank $\le n - 1$ . The maximal rank case has been well understood by De-Qi Zhang. We aim to characterize the pair $(X, G)$ such that $\operatorname {rank} G = n - 2$ .
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