Related papers: The Dynamical Degrees of Rational Surface Automorp…

We show that the topological full group of a Hausdorff ample groupoid with compact unit space coincides with the group of homotopy classes of invertible isometries in pseudofunction algebras associated with the groupoid. Moreover, if the…

To any finite graph $X$ (viewed as a topological space) we assosiate some explicit compact metric space ${\cal X}^r(X)$ which we call {\it the reflection tree of graphs $X$}. This space is of topological dimension $\le1$ and its connected…

Affine surfaces in $\mathbb{C}^{3}$ defined by an equation of the form $x^{n}z-Q(x,y)=0$ have been increasingly studied during the past 15 years. Of particular interest is the fact that they come equipped with an action of the additive…

A graph $X$ is defined inductively to be $(a_0,\dots,a_{n-1})$-regular if $X$ is $a_0$-regular and for every vertex $v$ of $X$, the sphere of radius $1$ around $v$ is an $(a_1,\dots,a_{n-1})$-regular graph. Such a graph $X$ is said to be…

Lehmer's number $\lambda_{10}$ is the smallest dynamical degree greater than $1$ that can occur for an automorphism of an algebraic surface. We show that $\lambda_{10}$ cannot be realized by automorphisms of Enriques surfaces in odd…

A Coxeter system is an ordered pair (W,S) where S is the generating set in a particular type of presentation for the Coxeter group W. A subgroup of W is called special if it is generated by a subset of S. Amalgamated product decompositions…

In this paper, it is shown that any surface automorphism of positive mapping-class entropy possesses a virtual homological eigenvalue which lies outside the unit circle of the complex plane.

We study classes of right-angled Coxeter groups with respect to the strong submodel relation of parabolic subgroup. We show that the class of all right-angled Coxeter group is not smooth, and establish some general combinatorial criteria…

We investigate the general structure of the automorphism group and the Lie algebra of derivations of a finitely generated vertex operator algebra. The automorphism group is isomorphic to an algebraic group. Under natural assumptions, the…

We study automorphism groups and birational automorphism groups of compact complex surfaces. We show that the automorphism group of such surface $X$ is always Jordan, and the birational automorphism group is Jordan unless $X$ is birational…

In this paper we consider the critical group of finite connected graphs which admit harmonic actions by the dihedral group $D_n$. In particular, we show that if the orbits of the $D_n$-action all have either $n$ or $2n$ points then the…

We show that the action of Cremona transformations on the real points of quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the torus, and of all non-orientable surfaces. The main result says that if X is rational,…

We construct examples of hyperKahler manifolds of Picard number two with automorphisms of positive entropy via derived automorphisms of K3 surfaces of Picard number one. Our hyperKahler manifolds are constructed as moduli spaces of…

An action of a group $G$ on an Enriques surface $S$ is called Mathieu if it acts on $H^0(2K_S)$ trivially and every element of order 2, 4 has Lefschetz number 4. A finite group $G$ has a Mathieu action on some Enriques surface if and only…

For every field $k$ of characteristic zero, we determine the groups that act as automorphisms on a smooth cubic surface over $k$. We also determine the groups that act on $k$-rational, stably $k$-rational, or $k$-unirational smooth cubic…

We prove the Morrison-Kawamata cone conjecture for klt Calabi-Yau pairs in dimension 2. That is, for a large class of rational surfaces as well as K3 surfaces and abelian surfaces, the action of the automorphism group of the surface on the…

A geometric charactrization of the equation found by Hietarinta and Viallet, which satisfies the singularity confinement criterion but which exhibits chaotic behavior, is presented. It is shown that this equation can be lifted to an…

In this paper we give an explicit description of the automorphism group of a primary Kodaira surface $X$ in terms of suitable liftings to the universal cover $\mathbb{C}^2$. As it happens for complex tori, the automorphism group of $X$ is…

We investigate the $C^0$-topology of the group of symplectic diffeomorphisms of positive symplectic rational surfaces. For all but a few exceptions, we prove that the group of Hamiltonian diffeomorphisms forms a connected component in the…

Based on the third author's thesis in this article we complete the local recognition of commuting reflection graphs of spherical Coxeter groups arising from irreducible crystallographic root systems.