Combinatorially formal arrangements are not determined by their points and lines
Combinatorics
2019-03-29 v1
Abstract
An arrangement of hyperplanes is called formal, if the relations between the hyperplanes are generated by relations in codimension 2. Formality is not a combinatorial property, raising the question for a characterization for combinatorial formality. A sufficient condition for this is if the underlying matroid has no proper lift with the same points and lines. We present an example of a matroid with such a lift but no non-formal realization, thus showing that above condition is not necessary for combinatorial formality.
Cite
@article{arxiv.1903.11925,
title = {Combinatorially formal arrangements are not determined by their points and lines},
author = {Tilman Moeller},
journal= {arXiv preprint arXiv:1903.11925},
year = {2019}
}
Comments
8 pages, 3 figures