Publication: Sylvester-Gallai Theorems for Complex Numbers and Quaternions
Loading...
Open/View Files
Date
2006
Published Version
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Verlag
The Harvard community has made this article openly available. Please share how this access benefits you.
Citation
Elkies, Noam D., Lou M. Pretorius, and Konrad J. Swanepoel. 2006. Sylvester-gallai theorems for complex numbers and quaternions. Discrete and Computational Geometry 35, (3): 361-373.
Abstract
A 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.
Description
Other Available Sources
Research Data
Keywords
Terms of Use
This article is made available under the terms and conditions applicable to Other Posted Material (LAA), as set forth at Terms of Service