Related papers: Jordan groups and algebraic surfaces

The classical Jordan curve theorem for digital curves asserts that the Jordan curve theorem remains valid in the Khalimsky plane. Since the Khalimsky plane is a quotient space of $\mathbb R^2$ induced by a tiling of squares, it is natural…

We generalize Abel's classical theorem on linear equivalence of divisors on a Riemann surface. For every closed submanifold $M^d \subset X^n$ in a compact oriented Riemannian $n$--manifold, or more generally for any $d$--cycle $Z$ relative…

In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real…

We introduce the notion of a graded group action on a graded algebra or, which is the same, a group action by graded pseudoautomorphisms. An algebra with such an action is a natural generalization of an algebra with a super- or a…

Let G be the group of rational points of a connected reductive group over a finite field. Based on work of Lusztig and Yun, we make the Jordan decomposition for irreducible G-representations canonical. It comes in the form of an equivalence…

We show that the Jordan decomposition of characters of finite reductive groups can be chosen so that if the centralizer of the relevant semisimple element in the dual group is connected, then the map is Galois-equivariant. Further, in this…

Recently George Bergman proved that the symmetric group of an infinite set possesses the following property which we call by the {\it universality of finite width}: given any generating set $X$ of the symmetric group of an infinite set…

We construct Jordan algebras over a locally ringed space using generalizations of the Tits process and the first Tits construction by Achhammer. Some general results on the structure of these algebras are obtained. Examples of Albert…

We study linear spaces of symmetric matrices whose reciprocal is also a linear space. These are Jordan algebras. We classify such algebras in low dimensions, and we study the associated Jordan loci in the Grassmannian.

We prove that if $\mathcal{A}$ is a complex, unital semisimple Banach algebra and $\mathcal{B}$ is a complex, unital Banach algebra having a separating family of finite-dimensional irreducible representations, then any unital linear…

We prove that the complex surfaces parametrizing cuboids and face cuboids, as well as their minimal resolution of singularities, have trivial fundamental group. We then compute the fundamental group of certain open smooth subvarieties of…

We introduce a new canonical height function for Jordan blocks of small eigenvalues for endomorphisms on smooth projective varieties over a number field. We prove that under an assumption on the eigenvalues of the endomorphism on the group…

Given a smooth hyperplane section $H$ of a rational homogeneous space $G/P$ with Picard number one, we address the question whether it is always possible to lift an automorphism of $H$ to the Lie group $G$, or more precisely to Aut$(G/P)$.…

We prove that simple, thick hyperbolic P-manifolds of dimension >2 exhibit Mostow rigidity. We also prove a quasi-isometry rigidity result for the fundamental groups of simple, thick hyperbolic P-manifolds of dimension >2. The key tool in…

We classify rational surfaces for which the image of the automorphisms group in the group of linear transformations of the Picard group is the largest possible. This answers a question raised by Arthur Coble in 1928, and can be rephrased in…

We consider polynomials that are orthogonal over an analytic Jordan curve L with respect to a positive analytic weight, and show that each such polynomial of sufficiently large degree can be expanded in a series of certain integral…

A geometric realization of the projective completion of the Jordan pair corresponding to a three-graded Lie algebra is given which permits to develop a geometric structure theory of the projective completion. This will be used in Part II of…

In universal algebraic geometry the category of the finite generated free algebras of some fixed variety of algebras and the quotient group A/Y are very important. Here A is a group of all automorphisms of this category and Y is a group of…

This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…

The Bonnaf\'e-Rouquier equivalence can be seen as a modular analogue of Lusztig's Jordan decomposition for groups of Lie type. In this paper, we show that this equivalence can be lifted to include automorphisms of the finite group of Lie…