Projektive G-Faserräume

authored by

Herbert Hotje

Abstract

Let σ > 0 be an integer. A projective σ-fibre space is formed by a covering of a projective geometry with σ-1 isomorphic geometries. The double elliptic space (Sphärischer Raum) is an example of a 2-fibre space. This note deals with projective σ-fibre spaces which are structured by multy valued orderfunctions (This notion was introduced by W. JUNKERS [2] for projective geometries) the range of which is a group G. If such an ordered σ-fibre space has the property |G|=σ, it is called projective G-fibre space. It is proved that the desarguesian projective G-fibre spaces V are exactly those, which are induced by a vector space S over a field K (commutative or not) having a normal subgroup P {normal subgroup of} K^*(·) with K^*′ ⊂P such that G≅K^*/P and S≅V^*/P. This theorem is a generalization of the well-known case P=K^*.

Organisation(s)

Institute of Algebraic Geometry

Type

Article

Journal

Journal of Geometry

Volume

1

Pages

69-89

No. of pages

21

ISSN

0047-2468

Publication date

03.1971

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Geometry and Topology

Electronic version(s)

https://doi.org/10.1007/BF02150276 (Access: Closed)