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Free abelian group actions on normal projective varieties: submaximal dynamical rank case

Part of: Surfaces and higher-dimensional varieties Automorphic functions Complex spaces with a group of automorphisms Topological dynamics Holomorphic mappings and correspondences

Published online by Cambridge University Press:  14 May 2020

Fei Hu  and
Sichen Li
Fei Hu
Affiliation:
University of British Columbia, Vancouver, BCV6T 1Z2, Canada and Pacific Institute for the Mathematical Sciences, Vancouver, BCV6T 1Z4, Canada Current address: University of Waterloo, Waterloo, ONN2L 3G1, Canada e-mail: hf@u.nus.edu URL: https://sites.google.com/view/feihu90s/
Sichen Li
Affiliation:
School of Mathematical Sciences, East China Normal University, 500 Dongchuan Road, Shanghai200241, China and Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore119076, Republic of Singapore Current address: School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai 200433, China e-mail: lisichen123@foxmail.com
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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 $\operatorname {rank} G = n - 2$ .

Keywords

Automorphismdynamical degreedynamical ranktopological entropyKodaira dimensionweak Calabi–Yau varietyspecial MRC fibration

MSC classification

Primary: 14J50: Automorphisms of surfaces and higher-dimensional varieties
Secondary: 32M05: Complex Lie groups, automorphism groups acting on complex spaces 32H50: Iteration problems 37B40: Topological entropy

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Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 4 , August 2021 , pp. 1057 - 1073
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Copyright
© Canadian Mathematical Society 2020

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