Constraints on automorphism groups of higher dimensional manifolds

Turgay Bayraktar (1) , Serge Cantat (2)

1 Syracuse University
2 IRMAR - Institut de Recherche Mathématique de Rennes

In this note, we prove, for instance, that the automorphism group of a rational manifold X which is obtained from CP^k by a finite sequence of blow-ups along smooth centers of dimension at most r with k>2r+2 has finite image in GL(H^*(X,Z)). In particular, every holomorphic automorphism $f:X\to X$ has zero topological entropy.

Mots clés: automorphism; rational manifold; topological entropy

Domaines: Systèmes dynamiques [math.DS]

Turgay Bayraktar, Serge Cantat. Constraints on automorphism groups of higher dimensional manifolds. Australian Journal of Mathematical Analysis and Applications, 2013, 405 (1), pp.209-213. ⟨10.1016/j.jmaa.2013.03.048⟩. ⟨hal-01169341⟩