Holomorphic actions, Kummer examples, and Zimmer program

Serge Cantat; Abdelghani Zeghib

Annales scientifiques de l'École Normale Supérieure (2012)

  • Volume: 45, Issue: 3, page 447-489
  • ISSN: 0012-9593

Abstract

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

How to cite

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Cantat, Serge, and Zeghib, Abdelghani. "Holomorphic actions, Kummer examples, and Zimmer program." Annales scientifiques de l'École Normale Supérieure 45.3 (2012): 447-489. <http://eudml.org/doc/272153>.

@article{Cantat2012,
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 complex tori as compact Kähler manifolds with large automorphisms groups.},
author = {Cantat, Serge, Zeghib, Abdelghani},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {lattices; superrigidity; complex tori; automorphism groups; Hodge theory; invariant cones; holomorphic dynamics},
language = {eng},
number = {3},
pages = {447-489},
publisher = {Société mathématique de France},
title = {Holomorphic actions, Kummer examples, and Zimmer program},
url = {http://eudml.org/doc/272153},
volume = {45},
year = {2012},
}

TY - JOUR
AU - Cantat, Serge
AU - Zeghib, Abdelghani
TI - Holomorphic actions, Kummer examples, and Zimmer program
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2012
PB - Société mathématique de France
VL - 45
IS - 3
SP - 447
EP - 489
AB - 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 complex tori as compact Kähler manifolds with large automorphisms groups.
LA - eng
KW - lattices; superrigidity; complex tori; automorphism groups; Hodge theory; invariant cones; holomorphic dynamics
UR - http://eudml.org/doc/272153
ER -

References

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