0000000000082453
AUTHOR
Armin Herzer
�ber rationale Darstellungen von Kettengeometrien als projektive Variet�ten
Der Satz von Tits für PGL2(R), R ein kommutativer Ring vom stabilen Rang 2
Certain permutation groups on sets with distance relation are characterized as groups of projectivities PGL2(R) on the projective line over a commutative ring R of stable rank 2, thus generalizing a classical result of Tits where R is a field.
Ein Axiomensystem f�r partielle affine R�ume
A partial linear space with parallelism is called partial affine space if it is embeddable in an affine space with the same pointset preserving the parallelism. These partial affine spaces will be characterized by a system of three axioms for partial linear spaces with parallelism.
B�schels�tze zur Charakterisierung projektiv darstellbarer Zykelebenen
Lineare Kongruenzen, die aus freien zyklischen Moduln halbeinfacher Algebren bestehen
Dualit�ten mit zwei Geraden aus absoluten Punkten in projektiven Ebenen
Charakterisierung regul�rer Faserungen durch Schlie�ungss�tze
�ber niedrigdimensionale projektive Darstellungen von Kettengeometrien
Characterization of strong chain geometries by their automorphism group
A wide class of chain geometries is characterized by their automorphism group using properties of a distinguished involution.
The generalized André systemsA(F,ß,(gi), (f i), ε)
Charakterisierung von Kettengeometrien �ber semilokalen Algebren
Chain geometries over semilocal rings are characterized as special touching structures possessing a distinguished group of automorphisms fixing two distant points.
Zu einem Satz von H. Lüneburg über verallgemeinerte André-Ebenen
On sets of subspaces closed under reguli
Using a representation of chain geometries where points are certain subspaces of a projective space and chains are reguli, we give an algebraic description of the weak subspaces of the chain geometry (i.e. the subsets of the pointset which are closed with respect to reguli).
Semimodular Locally Projective Lattices of Rank 4 from v.Staudt’s Point of View
We consider groups of projectivities in a certain kind of lattices called “Spaces”,also comprising the circle planes, and give theorems of v.Staudtian type, which characterize those Spaces which can be represented by a sublattice of a projective geometry of rank 4.
On a projective representation of chain geometries
We define a distance d on the set of r-spaces of an n-space. By the transfer of d to the GrasmannianG=G(n, r) we obtain a distinguished class of normal rational curves of order 1, the “1-distance lines’, 1=1,..., r, which are in 1–1-correspondence to the so-called “generalized reguli of type (r, 1)”.
Über den Rang der projektiven Darstellung von Kettengeometrien auf Grassmann-Mannigfaltigkeiten
Erg�nzung zu ?�ber rationale Darstellungen von Kettengeometrien als projektive Variet�ten?
Endliche nichtkommutative Gruppen mit PartitionII und fixpunktfreiemII-Automorphismus
Kollineationen und Schliessungssätze für Ebene Faserungen
Every affine central collineation of a translation plane π induces a special collineation of the projective space π spanned by the spreadF belonging to π. Here the relations between these special collineations of π and certain incidence propositions inF are investigated; so new proofs are given for some characterisations of (A,B)-regular spreads included in [7].
Characterization of chain geometries of finite dimension by their automorphism group
A large class of chain geometries of finite dimension is characterized as strong chain spaces possessing a distinguished group of automorphisms fixing two distant points.
On Finite Translation Structures with Proper Dilatations
Recently, Biliotti and the author obtained a certain number of results on translation structures with proper dilatations including structure-and characterisation-theorems, which here will be reformulated in a different manner, throwing a new light on some of the regarded questions.
Affine Kettengeometrien �ber Jordanalgebren
It is shown that an affine chain geometry over a Jordan algebra can be constructed in a nearly classical manner. Conversely, such chain geometries are characterized as systems of rational normal curves having a group of automorphisms with certain properties.
Translationsstrukturen, die weder axial noch zentral sind
Synthetische Konstruktion affiner M�biusgeometrien
Zur Geometrie der Translationsstrukturen mit eigentlichen Dilatationen
�ber Kreisebenen mit Potenzlinie
Die Schmieghyperebenen an die Veronese-Mannigfaltigkeit bei Beliebiger Charakteristik
By means of linear algebra a base-free definition of a Veronese variety V(n,r) is given and also an illuminating description of its osculating primes from which can be deduced in a general form and without difficulty the phenomena of degeneracy in case of small characteristics. (Instance best known: For characteristic 2 all tangents of a conic are confluent.) The last section investigates special problems for the V(1,r) in characteristic p: So the osculating primes of a V(1,p) intersect its node in a V(1,p-2). Furthermore it becomes clearer why for 2<r<¦K¦−1 no elation can fix a V(1,r) (in case of a perfect field).
Ein Kriterium f�r Quasik�rperA(F, ?, (g i ), (f i ),n)
Eine Beziehung zwischen Regularitätsbedingungen für Faserungen
This is the proof of a theorem which states a relation between some regularity conditions for spreads.