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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… Expand

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… Expand

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… Expand

Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups

- Serge Cantat, Serge Keiji 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… Expand

Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy

- Serge Cantat, C. Dupont
- Mathematics
- 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… Expand

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… Expand

The Cremona group in two variables

- Serge Cantat
- Mathematics
- 2012

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

- T. Bayraktar, Serge Cantat
- Mathematics
- 15 December 2012

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 r… Expand

Morphisms between Cremona groups, and characterization of rational varieties

- Serge Cantat
- Mathematics
- Compositio 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… Expand

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