Dynamical degrees of birational transformations of projective surfaces

Blanc, Jérémy¹ ; Cantat, Serge²

¹ Mathematisches Institut, Universität Basel, Spiegelgasse 1, 4051 Basel, Switzerland
² IRMAR, UMR 6625 du CNRS, Université de Rennes I, 35042 Rennes, France

Journal of the American Mathematical Society, Tome 29 (2016) no. 2, pp. 415-471

Résumé

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.

Détail

DOI : 10.1090/jams831

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