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
Tag:Translation planes ; ovoids ; quadratic forms
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):11H55 Quadratic forms (reduction theory, extreme forms, etc.)
51E15 Affine and projective planes

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