Projective deformations of congruences of planes in $n$-dimensional projective space

Projective planes over quadratic 2-dimensional algebras

The split version of the Freudenthal-Tits magic square stems from Lie theory and constructs a Lie algebra starting from two split composition algebras [5, 20, 21]. The geometries appearing in the second row are Severi varieties [24]. We provide an easy uniform axiomatization of these geometries and related ones, over an arbitrary field. In particular we investigate the entry A2 × A2 in the magi...

Projective Planes of Type

During the last few years, there has been a mild surge of interest in projective planes of type I-4. This paper is intended to both provide a survey of some recent theorems, and to present some new results concerning these planes. In Section 2, we describe the algebraic setting for these planes. Special attention is given to the structure of the relevant homology groups. In Section 3, some rece...

Projective Planes in Algebraically

We investigate the combinatorial geometry obtained from algebraic closure over a fixed subfield in an algebraically closed field. The main result classifies the subgeometries which are isomorphic to projective planes. This is applied to give new examples of algebraic characteristic sets of matroids. The main technique used, which is motivated by classical projective geometry, is that a particul...

Mirror Symmetry for Weighted Projective Planes and Their Noncommutative Deformations

Embeddings of Projective Klingenberg Planes in the Projective Space PG(5,K)

In this paper embeddings of projective Klingenberg planes in a 5-dimensional projective space are classified. It is proved that if a PK-plane is fully embedded in PG(5,K), for some skewfield K, then it is either isomorphic to the Desarguesian projective Klingenberg plane (projective Hjelmslev plane for bijective σ) PH(2,D(K, σ)) over a ring of ordinary or twisted dual numbers or it is a subgeom...