New Examples of Oriented Matroids with Disconnected Realization Spaces
We construct oriented matroids of rank 3 on 13 points whose realization spaces are disconnected. They are defined on smaller point-sets than the known examples with this property. Moreover, we construct one on 13 points whose realization space is a connected but non-irreducible semialgebraic variety.
KeywordsOriented matroids Realization space