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Dynamical degrees of birational transformations of projective surfaces
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 allExpand
Invariant hypersurfaces in holomorphic dynamics
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 dominantExpand
Normal subgroups in the Cremona group
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 strategyExpand
Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups
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 coneExpand
Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy
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
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 commeExpand
Rational surfaces with a large group of automorphisms
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 byExpand
The Cremona group in two variables
We survey a few results concerning the Cremona group in two variables. 2010 Mathematics Subject Classification. Primary 14E07 ; Secondary 20E32, 32M05, 37F99.
Constraints on automorphism groups of higher dimensional manifolds
In this note, we prove, for instance, that the automorphism group of a rational manifold X which is obtained from CP^k by a finite sequence of blow-ups along smooth centers of dimension at most rExpand
Morphisms between Cremona groups, and characterization of rational varieties
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 \geqExpand