Holomorphic actions, Kummer examples, and Zimmer Program

Abstract

We classify compact Kähler manifolds $M$ of dimension $n\ge 3$ on which acts a lattice of an almost simple real Lie group of rank $\ge n-1$. This provides a new line in the so-called Zimmer program, and characterizes certain type of complex tori by a property of their automorphisms groups.

35 pages