Sylvester-Gallai Theorems for Complex Numbers and Quaternions

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dc.creatorElkies, Noam
dc.creatorPretorius, Lou M.
dc.creatorSwanepoel, Konrad J.
dc.date2004-03-01
dc.date2006-02-15
dc.date.accessioned2026-07-07T06:36:00Z
dc.date.available2026-07-07T06:36:00Z
dc.descriptionA Sylvester-Gallai (SG) configuration is a finite set S of points such that the line through any two points in S contains a third point of S. According to the Sylvester-Gallai Theorem, an SG configuration in real projective space must be collinear. A problem of Serre (1966) asks whether an SG configuration in a complex projective space must be coplanar. This was proved by Kelly (1986) using a deep inequality of Hirzebruch. We give an elementary proof of this result, and then extend it to show that an SG configuration in projective space over the quaternions must be contained in a three-dimensional flat.
dc.description13 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0403023
dc.identifierhttp://arxiv.org/abs/math/0403023
dc.identifierDiscrete & Computational Geometry 35 (2006), no. 3, 361--373
dc.identifierdoi:10.1007/s00454-005-1226-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99962
dc.subjectMetric Geometry
dc.subjectCombinatorics
dc.subject52C35; 52C10
dc.titleSylvester-Gallai Theorems for Complex Numbers and Quaternions
dc.typetext

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