Automorphisms of rational surfaces with positive entropy

Julie Deserti (1) , Julien Grivaux (2, 3, 4)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 Department of Mathematics [Imperial College London]
3 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
4 LATP - Laboratoire d'Analyse, Topologie, Probabilités

A complex compact surface which carries an automorphism of positive topological entropy has been proved by Cantat to be either a torus, a K3 surface, an Enriques surface or a rational surface. Automorphisms of rational surfaces are quite mysterious and have been recently the object of intensive studies. In this paper, we construct several new examples of automorphisms of rational surfaces with positive topological entropy. We also explain how to define and to count parameters in families of birational maps of the complex projective plane and in families of rational surfaces.

Mots clés: automorphisms of rational surfaces; positive topological entropy; families of birational maps

Domaines: Géométrie algébrique [math.AG]; Systèmes dynamiques [math.DS]

Julie Deserti, Julien Grivaux. Automorphisms of rational surfaces with positive entropy. Indiana University Mathematics Journal, 2011, 60 (5), pp.1589--1622. ⟨10.1512/iumj.2011.60.4427⟩. ⟨hal-01301377⟩