Groupes commutatifs d'automorphismes d'une variete Kahlerienne compacte

2002/12/05 by T. C. Dinh, Dinh, T. C., N. Sibony +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.math/0212081

18 pages, nouvelle version

arxiv created 2002/12/05 · arxiv updated 2009/11/30

Abstract

Let V be a compact Kahler manifold. Let G' be a commutative subgroup of Aut(V) and U the set of elements of zero entropy of G'. Then U is a group and G' is isomorphic to the direct product of groups U and G where G is a subgroup of G' such that all elements of G, except the identity, are of positive entropy. Moreover, G is a free commutative group with rank(G)<dim(V). The estimate is sharp. When rank(G)=dim(V)-1, U is finite. Rank(G) satisfies other inequalities involving the dimensions of Dolbeault cohomology groups of V.

Related

• Solvable automorphism groups of a compact Kaehler manifold
• On the virtual invariants of zero entropy groups of compact Kähler manifolds
• Automorphisms of hyperkähler manifolds in the view of topological entropy
• Exponential mixing of all orders and CLT for automorphisms of compact Kähler manifolds
• The Rank Theorem and L²-invariants in Free Entropy: Global Upper Bounds