Related papers: Dynamical degrees of (pseudo)-automorphisms fixing…

We study the group of automorphisms of the affine plane preserving some given curve, over any field. The group is proven to be algebraic, except in the case where the curve is a bunch of parallel lines. Moreover, a classification of the…

We produce first examples of p-local height three TAF homology theories. The corresponding one-dimensional formal groups arise as split summands of the formal groups of certain abelian three-folds, the Shimura variety of which can be…

We give a classification of finite groups of symplectic birational automorphisms on a manifold of K3^[3]-type with stable and stably saturated cohomological action. We describe the group of polarized automorphisms of a smooth double…

In this article we give two explicit families of automorphisms of degree $\leq 3$ of the affine $3$-space $\mathbb{A}^3$ such that each automorphism of degree $\leq 3$ of $\mathbb{A}^3$ is a member of one of these families up to composition…

A few facts concerning the phrase "the automorphism groups become larger at special points of the moduli of K3 surfaces" are presented. It is also shown that the automorphism groups are of infinite order over a dense subset in any…

In this paper, let k be the affine n-space over an arbitrary field k. We show that dynamical degrees of affine-triangular automorphisms in dimension 4 are algebraic integers of degree not larger than 4. As a consequence, if char(k) is not…

We prove that every Salem number can be realized as the first dynamical degree of an automorphism of a complex simple abelian variety. Also by using the similar technique, we prove that the set of first dynamical degrees of automorphisms of…

The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being…

We consider a normal complete rational variety with a torus action of complexity one. In the main results, we determine the roots of the automorphism group and give an explicit description of the root system of its semisimple part. The…

In this paper we give a complete description of all possible automorphism groups of real $\mathbb{R}$-rational del Pezzo surfaces $X$ of degree $4$, using the description of $X$ as the blow-up of some smooth real quadric surface $Q$ in…

We define arithmetical and dynamical degrees for dynamical systems with several rational maps on projective varieties, study their properties and relations, and prove the existence of a canonical height function associated with divisorial…

Given integers $d\ge 3$ and $N\ge 3$. Let $G$ be a finite abelian group acting faithfully and linearly on a smooth hypersurface of degree $d$ in the complex projective space $\mathbb{P}^{N-1}$. Suppose $G\subset PGL(N, \mathbb{C})$ can be…

In this paper, we develop a new method to classify abelian automorphism groups of hypersurfaces. We use this method to classify (Theorem 4.2) abelian groups that admit a liftable action on a smooth cubic fourfold. A parallel result (Theorem…

We construct an example of a birational transformation of a rational threefold for which the first and second dynamical degrees coincide and are $>1$, but which does not preserve any holomorphic (singular) foliation. In particular, this…

We study domains in complex $n$-space with automorphism group that does not depend on the full $n$ dimensions of the ambient space. A sufficient geometric condition is obtained to guarantee that a domain has such a "thin" automorphism…

We classify the group of birational automorphisms of Hilbert schemes of points on algebraic K3 surfaces of Picard rank one. We study whether these automorphisms are symplectic or non-symplectic and if there exists a hyperk\"ahler birational…

Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the automorphism group on these hypersurfaces. We prove that…

Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…

We consider the class of quasiprojective varieties admitting a dominant morphism onto a curve with negative Euler characteristic. The existence of such a morphism is a property of the fundamental group. We show that for a variety in this…

We consider the minimum value of the first dynamical degrees, which are larger than $1$, of automorphisms for prime dimensional complex simple abelian varieties. Also, we calculate the minimum value of the first dynamical degrees, which are…