Automorphisms of compact Kähler manifolds with slow dynamics
Authors:
Serge Cantat and Olga Paris-Romaskevich
Journal:
Trans. Amer. Math. Soc. 374 (2021), 1351-1389
MSC (2020):
Primary 14H37, 37A35
DOI:
https://doi.org/10.1090/tran/8229
Published electronically:
November 2, 2020
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Abstract | References | Similar Articles | Additional Information
Abstract: We study automorphisms of compact Kähler manifolds having slow dynamics. Adapting Gromov's classical argument, we give an upper bound on the polynomial entropy and study its possible values in dimensions and
. We prove that every automorphism with sublinear derivative growth is an isometry; a counter-example is given in the
context, answering negatively a question of Artigue, Carrasco-Olivera, and Monteverde in [Acta Math. Hungar. 152 (2017), pp. 140-149] on polynomial entropy. We also study minimal automorphisms of surfaces with respect to the Zariski or euclidean topology.
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Additional Information
Serge Cantat
Affiliation:
Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France
Email:
serge.cantat@univ-rennes1.fr
Olga Paris-Romaskevich
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
Email:
olga@pa-ro.net; olga.romaskevich@math.cnrs.fr
DOI:
https://doi.org/10.1090/tran/8229
Received by editor(s):
February 16, 2020
Received by editor(s) in revised form:
February 16, 2020, and June 24, 2020
Published electronically:
November 2, 2020
Article copyright:
© Copyright 2020
American Mathematical Society