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arXiv · 1903.11925

Combinatorially formal arrangements are not determined by their points and lines

Tilman Moeller
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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.

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Tilman Moeller. 2019-03-28. Combinatorially formal arrangements are not determined by their points and lines. https://arxiv.org/abs/1903.11925

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