Invariant measures for large automorphism groups of projective surfaces

Serge Cantat (1) , Romain Dujardin (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

We classify invariant measures for non-elementary groups of automorphisms, on any compact Kähler surface X, under the assumption that the group contains a so-called "parabolic automorphism". We also provide finiteness results for the number of invariant, ergodic, probability measures with a Zariski dense support.

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

Serge Cantat, Romain Dujardin. Invariant measures for large automorphism groups of projective surfaces. Transformation Groups, In press, ⟨10.1007/s00031-022-09782-0⟩. ⟨hal-03371645⟩