相关论文: Automorphisms of A1-fibered surfaces

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

For a relatively minimal surface fibration $f: X\to C$, the equivariant automorphism group of $f$ is, roughly speaking, the group of automorphisms of $X$ preserving the fibration structure. We present a classification of such fibrations of…

We consider fibrations by affine lines on smooth affine surfaces obtained as complements of smooth rational curves $B$ in smooth projective surfaces $X$ defined over an algebraically closed field of characteristic zero. We observe that…

For a complex surface of general type with a relatively minimal genus 2 fibration, the bounds of the orders of the automorphism group of the fibration, of its abelian subgroups and of its cyclic subgroups are determined as linear functions…

We show that the automorphism group of a certain subclass of smooth Gizatullin surfaces with a distinguished and rigid extended divisor is generated by automorphisms of A1-fibrations. Moreover, such surfaces provide examples of smooth…

We study automorphism groups of fibered surfaces for finite cyclic covering fibrations of an elliptic surface. We estimate the order of a finite subgroup of automorphism groups in terms of the genus of the fiber, the genus of the base…

We calculate the automorphism group of certain Enriques surfaces. The Enriques surfaces that we investigate include very general $n$-nodal Enriques surfaces and very general cuspidal Enriques surfaces. We also describe the action of the…

We consider a one-dimensional family of rational surfaces with automorphisms. In a degeneration of this family, the limiting map is the identity map on a special fiber. We check that the map on the total space of the family has…

The fine 1-curve graph of a surface is a graph whose vertices are simple closed curves on the surface and whose edges connect vertices that intersect in at most one point. We show that the automorphism group of the fine 1-curve graph is…

We study slopes of finite cyclic covering fibrations of a fibered surface. We give the best possible lower bound of the slope of these fibrations. We also give the slope equality of finite cyclic covering fibrations of a ruled surface and…

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such…

For a geometrically rational surface X over an arbitrary field of characteristic different from 2 and 3 that contains all roots of 1, we show that either X is birational to a product of a projective line and a conic, or the group of…

We study orbit closures and stationary measures for groups of automorphisms of $p$-adic affine surfaces.

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…

The generators of the group of birational automorphisms of any Severi-Brauer surface non-isomorphic over an algebraically non-closed field to the projective plane are explicitly described.

We study automorphism groups of formal matrix algebras. We also consider automorphisms of ordinary matrix algebras (in particular, triangular matrix algebras).

Every indefinite binary form occurs as the Picard lattice of some K3-surface. The group of its isometries, or automorphs, coincides with the automorphism group of the K3-surface, but only up to finite groups. The classical theory of…

In this note we define fibrations of topological stacks and establish their main properties. We prove various standard results about fibrations (fiber homotopy exact sequence, Leray-Serre and Eilenberg-Moore spectral sequences, etc.). We…

We construct k-parameter families of rational surface automorphisms for any k. These are automorphisms of surfaces X, which are constructed from iterated blowups over the projective plane. In certain cases: we are able to determine the…

We obtain analogues of classical results on automorphism groups of holomorphic fiber bundles, in the setting of group schemes. Also, we establish a lifting property of the connected automorphism group, for torsors under abelian varieties.…