Related papers: Automorphisms of del Pezzo surfaces without points
We study the birational properties of geometrically rational surfaces from a derived categorical point of view. In particular, we give a criterion for the rationality of a del Pezzo surface over an arbitrary field, namely, that its derived…
In this paper we compute the Jordan constants of the Cremona group of rank two over all fields of characteristic zero.
We investigate automorphism groups of planar graphs. The main result is a complete recursive description of all abstract groups that can be realized as automorphism groups of planar graphs. The characterization is formulated in terms of…
We develop a geometric theory for difference equations with a given group of automorphisms. To solve this problem we extend the class of difference fields to the class of absolutely flat simple difference rings called pseudofields. We prove…
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 study automorphisms of the affine line over rings like ZZ/p^n.
Let $W$ be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that $W$ is birational to a product of a smooth projective variety $A$ and the projective line. We prove that if $A$ contains no rational…
In this paper we provide the complete classification of $\mathbb{P}^1$-bundles over smooth projective rational surfaces whose neutral component of the automorphism group is maximal. Our results hold over any algebraically closed field of…
We consider rational projective homogeneous varieties over an algebraically closed field of positive characteristic, namely quotients of a semi-simple group by a possibly non-reduced parabolic subgroup. We determine the group scheme…
The group of automorphisms is found for the Lie algebra of polynomial vector fields with constant divergence.
We study the biregular and birational geometry of degree 6 del Pezzo surfaces with Picard number 1, defined over an arbitrary perfect field. Using Galois cohomology techniques, we obtain an explicit description of cocycles for such surfaces…
We classify smooth weak del Pezzo surfaces with global vector fields over an arbitrary algebraically closed field $k$ of arbitrary characteristic $p \geq 0$. We give a complete description of the configuration of $(-1)$- and $(-2)$-curves…
We describe the effect of rational singularities on the Brauer group of a surface, and compute the Brauer groups of all singular del Pezzo surfaces over an algebraically closed field.
We construct the first examples of regular del Pezzo surfaces for which the irregularity (i.e. the dimension of the first cohomology group of the structure sheaf) is nonzero. We also find a restriction on the integer pairs that are possible…
We compute the exact values of the Jordan constants of abelian surfaces over finite fields.
We study singular del Pezzo surfaces that are quasi-smooth and well-formed weighted hypersurfaces. We give an algorithm how to classify all of them.
We construct absolutely simple jacobians of non-hyperelliptic genus 4 curves, using Del Pezzo surfaces of degree 1. This paper is a natural continuation of author's paper math.AG/0405156.
We compute and provide a detailed description on the Jordan constants of the multiplicative subgroup of quaternion algebras over number fields of small degree. As an application, we determine the Jordan constants of the multiplicative…
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 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…