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Dynamical degrees of birational transformations of projective surfaces
- J. Blanc, Serge Cantat
- Mathematics
- 1 July 2013
The dynamical degree lambda( f ) of a birational transformation f measures the exponential growth rate of the degree of the formulae that define the n -th iterate of f . We study the set of all…
Invariant hypersurfaces in holomorphic dynamics
- Serge Cantat
- Mathematics
- 2010
We prove the following result, which is analogous to two theorems, one due to Kodaira and Krasnov and another one due to Jouanolou and Ghys. Let M be a compact complex manifold and f a dominant…
Normal subgroups in the Cremona group
- Serge Cantat, St'ephane Lamy, Yves Cornulier
- Mathematics
- 6 July 2010
Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane $$ \mathbb{P}_{\mathbf{k}}^2 $$ is not a simple group. The strategy…
Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy
- Serge Cantat, C. Dupont
- MathematicsJournal of the European Mathematical Society
- 5 October 2014
We classify complex projective surfaces with an automorphism of positive entropy for which the unique invariant measure of maximal entropy is absolutely continuous with respect to Lebesgue measure.
Dynamics on Character Varieties and Malgrange irreducibility of Painlevé VI equation
- Serge Cantat, F. Loray
- Mathematics
- 2009
Nous etudions l'action du groupe modulaire sur l'espace des representations du groupe fondamental de la sphere privee de quatre points dans SL(2, ℂ). Ce systeme dynamique peut etre interprete comme…
Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups
- Serge Cantat, K. Oguiso
- Mathematics
- 29 July 2011
Thanks to the theory of Coxeter groups, we produce the first family of Calabi-Yau manifolds $X$ of arbitrary dimension $n$, for which ${\rm Bir}(X)$ is infinite and the Kawamata-Morrison movable cone…
Rational surfaces with a large group of automorphisms
- Serge Cantat, I. Dolgachev
- Mathematics
- 5 June 2011
We classify rational surfaces for which the image of the automorphisms group in the group of linear transformations of the Picard group is the largest possible. This answers a question raised by…
Morphisms between Cremona groups, and characterization of rational varieties
- Serge Cantat
- MathematicsCompositio Mathematica
- 25 June 2014
Abstract We classify all (abstract) homomorphisms from the group $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq…
Dynamics of automorphisms of compact complex surfaces
- Serge Cantat
- Mathematics
- 31 January 2014
Recent results concerning the dynamics of holomorphic diffeomorphisms of compact complex surfaces are described, that require a nice interplay between algebraic geometry, complex analysis, and…
Holomorphic actions, Kummer examples, and Zimmer Program
- Serge Cantat, A. Zeghib
- Mathematics
- 22 November 2010
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…
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