Line arrangements with many triple points
Combinatorics
2025-05-21 v1 Algebraic Geometry
Abstract
In this paper, we construct an infinite series of line arrangements in characteristic two, each featuring only triple intersection points. This finding challenges the existing conjecture that suggests the existence of only a finite number of such arrangements, regardless of the characteristic. Leveraging the theory of matroids and employing computer algebra software, we rigorously examine the existence and non-existence across various characteristics of line arrangements with up to 19 lines maximizing the number of triple intersection points.
Cite
@article{arxiv.2401.14766,
title = {Line arrangements with many triple points},
author = {Lukas Kühne and Tomasz Szemberg and Halszka Tutaj-Gasińska},
journal= {arXiv preprint arXiv:2401.14766},
year = {2025}
}
Comments
10 pages