Automorphism groups of positive entropy on projective Threefolds

Abstract

We prove two results about the natural representation of a group G of automorphisms of a normal projective threefold X on its second cohomology. We show that if X is minimal, then G, modulo a normal subgroup of null entropy, is embedded as a Zariski-dense subset in a semi-simple real linear algebraic group of real rank ≤ 2. Next, we show that X is a complex torus if the image of G is an almost abelian group of positive rank and the kernel is infinite, unless X is equivariantly non-trivially fibred. © 2013 American Mathematical Society.