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 points than the known examples with this property. Moreover, we construct the one on 13 points whose realization space is a connected and non-irreducible semialgebraic variety. 
Yasuyuki Tsukamoto
math.CO math.AG