Related papers: Automorphism groups of Inoue surfaces $S^{(+)}/S^{…

We determine explicitly the structure of the automorphism group of a parabolic Inoue surface. We also describe the quotients of the surface by typical cyclic subgroups of the automorphism group.

Using Lie groups with left-invariant complex structure, we construct new examples of compact complex manifolds with flat affine structure in arbitrarly high dimensions. In the 2-dimensional case, we retrieve the Inoue surfaces $S^+$.

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…

Let $S$ be a smooth minimal complex surface of general type with $p_g=0$ and $K^2=7$. We prove that any involution on $S$ is in the center of the automorphism group of $S$. As an application, we show that the automorphism group of an Inoue…

We give a characterization of Inoue surfaces in terms of automorphic pluriharmonic functions on a cyclic covering. Together with results of Chiose and Toma, this completes the classification of compact complex surfaces of Kaehler rank one.

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 give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.

We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup of Aut(S) generated by all its algebraic subgroups is not generated by any countable family of such subgroups,…

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 study quartic surfaces that admit a group of projective automorphisms isomorphic to icosahedron group.

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…

We prove some general results concerning the size of the group of automorphisms of the Douady space of points on a surface. We then study some properties of the automorphisms coming from an automorphism of the surface, in particular their…

In this note we show that if the automorphism group of a normal affine surface $S$ is isomorphic to the automorphism group of a Danielewski surface, then $S$ is isomorphic to a Danielewski surface.

We describe a set of generators and defining relations for the group of birational automorphisms of a general 15-nodal quartic surface in the complex projective 3-dimensional space.

We develop technics of birational geometry to study automorphisms of affine surfaces admitting many distinct rational fibrations, with a particular focus on the interactions between automorphisms and these fibrations. In particular, we…

We prove that automorphism groups of Inoue and primary Kodaira surfaces are Jordan.

We show that smooth hypersurfaces in complex projective spaces with automorphism groups of maximum size are isomorphic to Fermat hypersurfaces, with a few exceptions. For the exceptions, we give explicitly the defining equations and…

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…

We consider translation surfaces with poles on surfaces. We shall prove that any finite group appears as the automorphism group of some translation surface with poles. As a direct consequence we obtain the existence of structures achieving…

The special linear groups, the mapping class groups of surfaces, the outer autormorphism groups of free groups appear in numerous domains. Their analogies, developped in particular in K. Vogtmann's work, have been written about a lot. In…