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Holomorphic actions, Kummer examples, and Zimmer Program
Published 22 Nov 2010 in math.AG, math.DG, and math.DS | (1011.4768v1)
Abstract: 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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