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Applications of Number Theory to Ovoids and Translation Planes

  • In this paper we show that for each prime p=7 there exists a translation plane of order p^2 of Mason-Ostrom type. These planes occur as 6-dimensional ovoids being projections of the 8-dimensional binary ovoids of Conway, Kleidman and Wilson. In order to verify the existence of such projections we prove certain properties of two particular quadratic forms using classical methods form number theory.

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Author:Ulrich Dempwolff, Andreas Guthmann
URN (permanent link):urn:nbn:de:hbz:386-kluedo-8006
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (305)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Translation planes; ovoids; quadratic forms
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):11-XX NUMBER THEORY / 11Hxx Geometry of numbers (For applications in coding theory, see 94B75) / 11H55 Quadratic forms (reduction theory, extreme forms, etc.)
51-XX GEOMETRY (For algebraic geometry, see 14-XX) / 51Exx Finite geometry and special incidence structures / 51E15 Affine and projective planes
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011