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Affine Spaces within Projective Spaces

Affine spaces within projective spaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Nov 1999Embargo end date: 01 Jan 2013Publisher:Springer Science and Business Media LLCJournal:Results in Mathematics, volume 36, pages 237-251 (issn: 1422-6383, eissn: 1420-9012,

Authors: Andrea Blunck; Hans Havlicek;

doi: 10.1007/bf03322113 , 10.48550/arxiv.1304.0093

arXiv: http://arxiv.org/abs/1304.0093

Affine Spaces within Projective Spaces

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Abstract

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 reguli or cones over affine reguli. Moreover, we apply our concepts to the problem of describing dual spreads. We do not assume that the projective space is finite-dimensional or pappian.

Related Organizations

TU Wien
Austria

Keywords

dual spread, Mathematics - Rings and Algebras, Desarguesian and Pappian geometries, Mathematics - Algebraic Geometry, Incidence structures embeddable into projective geometries, regulus, Rings and Algebras (math.RA), Translation planes and spreads in linear incidence geometry, FOS: Mathematics, 51A30, 51A40, 51A45, Algebraic Geometry (math.AG), affine space

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FWF| Chain Geometries over Skew Fields