MEROMORPHIC LIMITS OF AUTOMORPHISMS

Let X be a compact complex manifold in the Fujiki class b. We study the compactification of Aut(0)(X) given by its closure in Barlet cycle space. The boundary points give rise to non-dominant meromorphic self-maps of X. Moreover convergence in cycle space yields convergence of the corresponding meromorphic maps. There are analogous compactifications for reductive subgroups acting trivially on Alb X. If X is Kahler, these compactifications are projective. Finally we give applications to the action of Aut(X) on the set of probability measures on X. In particular we obtain an extension of the Furstenberg lemma to manifolds in the class b.