Holomorphic actions, Kummer examples, and Zimmer Program

Mathematics – Algebraic Geometry

Scientific paper

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35 pages

Scientific paper

We classify compact K\"ahler manifolds $M$ of dimension $n\geq 3$ on which
acts a lattice of an almost simple real Lie group of rank $\geq n-1$. 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.

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