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 $\le 2$. 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.

Locations

• arXiv (Cornell University) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View
• Transactions of the American Mathematical Society - View