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Dynamical degrees of birational transformations of projective surfaces


Authors: Jérémy Blanc and Serge Cantat
Journal: J. Amer. Math. Soc. 29 (2016), 415-471
MSC (2010): Primary 14E07; Secondary 37F10, 32H50
DOI: https://doi.org/10.1090/jams831
Published electronically: June 3, 2015
MathSciNet review: 3454379
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Abstract: The dynamical degree $ \lambda (f)$ of a birational transformation $ f$ measures the exponential growth rate of the degree of the formulas that define the $ n$th iterate of $ f$. We study the set of all dynamical degrees of all birational transformations of projective surfaces, and the relationship between the value of $ \lambda (f)$ and the structure of the conjugacy class of $ f$. For instance, the set of all dynamical degrees of birational transformations of the complex projective plane is a closed and well ordered set of algebraic numbers.


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Additional Information

Jérémy Blanc
Affiliation: Mathematisches Institut, Universität Basel, Spiegelgasse 1, 4051 Basel, Switzerland
Email: Jeremy.Blanc@unibas.ch

Serge Cantat
Affiliation: IRMAR, UMR 6625 du CNRS, Université de Rennes I, 35042 Rennes, France
Email: cantat@univ-rennes1.fr

DOI: https://doi.org/10.1090/jams831
Received by editor(s): July 1, 2013
Received by editor(s) in revised form: February 24, 2015
Published electronically: June 3, 2015
Additional Notes: The first author acknowledges support by the Swiss National Science Foundation Grant “Birational Geometry” PP00P2_128422 /1.
Both authors acknowledge support by the French National Research Agency Grant “BirPol,” ANR-11-JS01-004-01
Article copyright: © Copyright 2015 American Mathematical Society