44 citations · 633 across the 77 of their papers we have counts for
24 papers · 2 filters
Incidence and Combinatorial Properties of Linear Complexes
Hans Havlicek, Corrado Zanella
In this paper a generalisation of the notion of polarity is exhibited which allows to completely describe, in an incidence-geometric way, the linear complexes of -subspaces. A g…
The Betten-Walker spread and Cayley's ruled cubic surface
Hans Havlicek, Rolf Riesinger
We establish that, over certain ground fields, the set of osculating tangents of Cayley's ruled cubic surface gives rise to a (maximal partial) spread which is also a dual (maximal…
Isometries and Collineations of the Cayley Surface
Johannes Gmainer, Hans Havlicek
Let be Cayley's ruled cubic surface in a projective three-space over any commutative field . We determine all collineations fixing , as a set, and all cubic forms definin…
Transformations on the product of Grassmann spaces
Hans Havlicek, Mark Pankov
We describe all adjacency preserving bijections of certain products of Grassmann spaces.
On distant-isomorphisms of projective lines
Andrea Blunck, Hans Havlicek
We determine all distant-isomorphisms between projective lines over semilocal rings. In particular, for those semisimple rings that do not have a simple component which is isomorph…
On the axiomatics of projective and affine geometry in terms of line intersection
Hans Havlicek, Victor Pambuccian
By providing explicit definitions, we show that in both affine and projective geometry of dimension , considered as first-order theories axiomatized in terms of lines as th…
A Three-Dimensional Laguerre Geometry and Its Visualization
Hans Havlicek, Klaus List
We describe and visualize the chains of the 3-dimensional chain geometry over the ring ,
Radical parallelism on projective lines and non-linear models of affine spaces
Andrea Blunck, Hans Havlicek
We introduce and investigate an equivalence relation called "radical parallelism" on the projective line over a ring. It is closely related with the Jacobson radical of the underly…
On bijections that preserve complementarity of subspaces
Andrea Blunck, Hans Havlicek
The set of all -dimensional subspaces of a -dimensional vector space is endowed with two relations, complementarity and adjacency. We consider bijections from on…
Jordan homomorphisms and harmonic mappings
Andrea Blunck, Hans Havlicek
We show that each Jordan homomorphism of rings gives rise to a harmonic mapping of one connected component of the projective line over into the projective line over $…
The Dual of a Chain Geometry
Andrea Blunck, Hans Havlicek
We introduce and discuss the dual of a chain geometry. Each chain geometry is canonically isomorphic to its dual. This allows us to show that there are isomorphisms of chain geomet…
On automorphisms of flag spaces
Hans Havlicek, Klaus List, Corrado Zanella
We show that the automorphisms of the flag space associated with a 3-dimensional projective space can be characterized as bijections preserving a certain binary relation on the set…
Veronese Varieties over Fields with non-zero Characteristic: A Survey
Hans Havlicek
In the present survey we collect some recent results on nuclei of Veronese varieties and invariant subspaces of normal rational curves. We must assume, however, that the ground fie…
The Connected Components of the Projective Line over a Ring
Andrea Blunck, Hans Havlicek
The main result of the present paper is that the projective line over a ring is connected with respect to the relation "distant" if, and only if, is a -ring.
Projective Representations II. Generalized chain geometries
Andrea Blunck, Hans Havlicek
In this paper, projective representations of generalized chain geometries are investigated, using the concepts and results of part I. In particular, we study under which conditions…
On embedded products of Grassmannians
Hans Havlicek, Corrado Zanella
Let and be two Grassmannians. The standard embedding is obtained by combining the Plücker and Segre embeddings. Given a further embedding $η: Γ'\t…
Projective Representations I. Projective lines over rings
Andrea Blunck, Hans Havlicek
We discuss representations of the projective line over a ring with 1 in a projective space over some (not necessarily commutative) field . Such a representation is based upo…
On linear morphisms of product spaces
Alessandro Bichara, Hans Havlicek, Corrado Zanella
Let be a linear morphism of the product of two projective spaces and into a projective space. Let be the Segre embedding of such a product. In this pape…
Affine Spaces within Projective Spaces
Andrea Blunck, Hans Havlicek
We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine regu…
A Dimension Formula for the Nucleus of a Veronese Variety
Johannes Gmainer, Hans Havlicek
The nucleus of a Veronese variety is the intersection of all its osculating hyperplanes. Various authors have given necessary and sufficient conditions for the nucleus to be empty.…
Extending the Concept of Chain Geometry
Andrea Blunck, Hans Havlicek
We introduce the chain geometry over a ring with a distinguished subfield , thus extending the usual concept where has to be an algebra over . A chain is uni…
Nuclei of Normal Rational Curves
Johannes Gmainer, Hans Havlicek
A -nucleus of a normal rational curve in PG is the intersection over all -dimensional osculating subspaces of the curve (). It is well known that…
Projective lines over Jordan systems and geometry of Hermitian matrices
Andrea Blunck, Hans Havlicek
Any set of -Hermitian matrices of size over a field with involution gives rise to a projective line in the sense of ring geometry and a projective space in the…
Von Staudt's theorem revisited
Hans Havlicek
We establish a version of von Staudt's theorem on mappings which preserve harmonic quadruples for projective lines over (not necessarily commutative) rings with "sufficiently many"…