The ordinal of dynamical degrees  of birational maps of the projective plane

Anna Bot

doi:10.5802/crmath.540

Article de recherche - Géométrie algébrique, Systèmes dynamiques

The ordinal of dynamical degrees of birational maps of the projective plane
[L’ordinal des degrés dynamiques des transformations birationelles du plan projectif]

Anna Bot ¹

¹ Department of Mathematics and Computer Science, University of Basel, 4051 Basel, Switzerland

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 117-134.

Résumé
Abstract

Nous démontrons que l’ordinal des degrés dynamiques de toutes les transformations birationnelles du plan projectif complexe est $ω^{ω}$ .

We show that the ordinal of the dynamical degrees of all birational maps of the complex projective plane is $ω^{ω}$ .

Reçu le : 2022-09-01
Révisé le : 2022-12-09
Accepté le : 2023-07-14
Publié le : 2024-03-07

DOI : 10.5802/crmath.540

Classification : 37F10, 32H50, 14E07, 14E05
Mots clés : Dynamical degree, rational projective surfaces, ordinals

Affiliations des auteurs :

Anna Bot ¹

¹ Department of Mathematics and Computer Science, University of Basel, 4051 Basel, Switzerland

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Anna Bot},
     title = {The ordinal of dynamical degrees  of birational maps of the projective plane},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {117--134},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.540},
     language = {en},
}

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Anna Bot. The ordinal of dynamical degrees  of birational maps of the projective plane. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 117-134. doi : 10.5802/crmath.540. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.540/

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