Related papers: Groups acting on cubic surfaces in characteristic …

We study linearizability of actions of finite groups on cubic threefolds with nonnodal isolated singularities.

We investigate subgroups of SL (n,Z) which preserve an open nondegenerate convex cone in real n-space and admit in that cone as fundamental domain a polyhedral cone of which some faces are allowed to lie on the boundary. Examples are…

We show the existence of a rational surface automorphism of positive entropy with a given number of Siegel disks. Moreover, among automorphisms obtained from quadratic birational maps on the projective plane fixing irreducible cubic curves,…

It is proved that on a smooth algebraic variety, fibered into cubic surfaces over the projective line and sufficiently ``twisted'' over the base, there is only one pencil of rational surfaces -- that is, this very pencil of cubics. In…

We classify the transitive, effective, holomorphic actions of connected complex Lie groups on complex surfaces.

We determine all posible orders of automorphisms of finite order of complex K3 surfaces or of K3 surfaces in characteristic $p>3$. E.g., a positive integer $N$ is the order of an automorphism of a complex K3 surface if and only if…

We study automorphism groups of real del Pezzo surfaces, concentrating on finite groups acting minimally on them. As a result, we obtain a vast part of classification of finite subgroups in the real plane Cremona group.

We compare real and complex dynamics for automorphisms of rational surfaces that are obtained by lifting \chg{some} quadratic birational maps of the plane. In particular, we show how to exploit the existence of an invariant cubic curve to…

We classify Coble surfaces with finite automorphism group in arbitrary characteristic not equal to 2. There are exactly 9 isomorphism classes of such surfaces.

We present finite sets of generators of the full automorphism groups of three singular K3 surfaces, on which the alternating group of degree 6 acts symplectically. We also present a finite set of generators of the full automorphism group of…

We will consider a two dimensional "symmetric" subfamily of the four dimensional family of Fricke cubic surfaces. The main result is that such symmetric cubic surfaces arise as character varieties for the exceptional group of type G_2.…

We give a geometric characterization of finite rational groups. In particular, we prove that a finite group is rational if and only if there exists a finite geometry $\Gamma$ of type $I$ and action of $G$ on $\Gamma$ as a group of…

We classify the possible images of the action of the group of automorphisms of a smooth Fano threefold on its Picard group. We also study the first group cohomology of the Picard group for families of smooth Fano threefolds.

We give an upper bound for the essential dimension of a smooth unipotent algebraic group over an arbitrary field. We also show that over a field $k$ which is finitely generated over a perfect field, a smooth unipotent algebraic $k$-group is…

Our main result is the determination of the respective groups $ Aut_\mathbb{Z}(S) $ of cohomologically trivial automorphisms and $ Aut_\mathbb{Q}(S) $ of numerically trivial automorphisms for the reducible fake quadrics, that is, the…

In this paper, we discuss certain types of conformal/anticonformal actions of the generalized quasi-dihedral group $G_{n}$ of order $8n$, for $n\geq 2$, on closed Riemann surfaces, pseudo-real Riemann surfaces and compact Klein surfaces,…

Let S be a complex minimal surface of general type with irregularity q(S)=1 and Aut_0(S) the subgroup of automorphisms acting trivially on the cohomology ring with rational coefficients. In this paper we show that |Aut_0(S)|<=4, and if the…

Let $A$ be an abelian surface over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by a Weil polynomial $f_A$ of degree 4. We give a classification of the groups of $k$-rational points on varieties from this class in…

Let $G$ be a finite 2-group and $K$ be a field satisfying that (i) $\fn{char}K\ne 2$, and (ii) $\sqrt{a}\in K$ for any $a\in K$. If $G$ acts on the rational function field $K(x,y,z)$ by monomial $K$-automorphisms, then the fixed field…

We consider $\mu_p$- and $\alpha_p$-actions on RDP K3 surfaces (K3 surfaces with rational double point singularities allowed) in characteristic $p > 0$. We study possible characteristics, quotient surfaces, and quotient singularities. It…