Résultat de la recherche
Finite quasisimple groups acting on rationally connected threefolds
We show that the only finite quasi-simple non-abelian groups that can faithfully act on rationally connected threefolds are the following groups: $\mathfrak{A}_5$, $\operatorname{PSL}_2(\mathbf{F}_7)$, $\mathfrak{A}_6$, $\operatorname{SL}_2(\mathbf{F}_8)$, $\mathfrak{A}_7$, $\operatorname{PSp}_4(\mathbf{F}_3)$, $\operatorname{SL}_2(\mathbf{F}_{7})$, $2.\mathfrak{A}_5$, $2.\mathfrak{A}_6$, $3.\mathfrak{A}_6$ or $6.\mathfrak{A}_6$. All of these groups with a possible exception of $2.\mathfrak{A}_6$ and $6.\mathfrak{A}_6$ indeed act on some rationally connected threefolds.
Dynamical degrees of affine-triangular automorphisms of affine spaces
AbstractWe study the possible dynamical degrees of automorphisms of the affine space$\mathbb {A}^n$. In dimension$n=3$, we determine all dynamical degrees arising from the composition of an affine automorphism with a triangular one. This generalizes the easier case of shift-like automorphisms which can be studied in any dimension. We also prove that each weak Perron number is the dynamical degree of an affine-triangular automorphism of the affine space$\mathbb {A}^n$for somen, and we give the best possiblenfor quadratic integers, which is either$3$or$4$.
Automorphisms of P1-bundles over rational surfaces
In this paper we provide the complete classification of $\mathbb{P}^1$-bundles over smooth projective rational surfaces whose neutral component of the automorphism group is maximal. Our results hold over any algebraically closed field of characteristic zero.
Connected Algebraic Groups Acting on three-dimensional Mori Fibrations
We study the connected algebraic groups acting on Mori fibrations $X \to Y$ with $X$ a rational threefold and $\textrm{dim}(Y) \geq 1$. More precisely, for these fibre spaces, we consider the neutral component of their automorphism groups and study their equivariant birational geometry. This is done using, inter alia, minimal model program and Sarkisov program and allows us to determine the maximal connected algebraic subgroups of $\textrm{Bir}(\mathbb{P}^3)$, recovering most of the classification results of Hiroshi Umemura in the complex case.