Ordinary lines in space
Combinatorics
2018-03-28 v1
Abstract
We prove that if a finite point set in real space does not have too many points on a plane, then it spans a quadratic number of ordinary lines. This answers the real case of a question of Basit, Dvir, Saraf, and Wolf. It shows that there is a significant difference in terms of ordinary lines between planar point sets, which may span a linear number of ordinary lines, and truly three-dimensional point sets. Our proof uses a projection argument of Kelly combined with a theorem of Beck on the number of spanned lines of a planar point set.
Cite
@article{arxiv.1803.09524,
title = {Ordinary lines in space},
author = {Frank de Zeeuw},
journal= {arXiv preprint arXiv:1803.09524},
year = {2018}
}