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Caractérisation des exemples de Lattès et de Kummer

Part of: Birational geometry Surfaces and higher-dimensional varieties Smooth dynamical systems: general theory Complex dynamical systems

Published online by Cambridge University Press:  01 September 2008

Serge Cantat
Serge Cantat*
Affiliation:
IRMAR, UMR 6625 du CNRS, Université de Rennes I, 35042 Rennes, France (email: serge.cantat@univ-rennes1.fr)
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Abstract

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Lattès and Kummer examples are rational transformations of compact kähler manifolds that are covered by an affine transformation of a compact torus. We present a few ergodic characteristic properties of these examples. The main results concern the case of surfaces.

Keywords

holomorphic dynamicsalgebraic surfacesLattès examples

MSC classification

Secondary: 37C40: Smooth ergodic theory, invariant measures 37F99: None of the above, but in this section 14J28: $K3$ surfaces and Enriques surfaces 14J32: Calabi-Yau manifolds 14J50: Automorphisms of surfaces and higher-dimensional varieties 14E05: Rational and birational maps
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 5 , September 2008 , pp. 1235 - 1270
Copyright
Copyright © Foundation Compositio Mathematica 2008

References

Supported by the ANR project Symplexe.