Moduli Spaces of Arrangements of 10 Projective Lines with Quadruple   Points
  We classify moduli spaces of arrangements of 10 lines with quadruple points. We show that moduli spaces of arrangements of 10 lines with quadruple points may consist of more than 2 disconnected components, namely 3 or 4 distinct points. We also present defining equations to those arrangements whose moduli spaces are still reducible after taking quotients of complex conjugations. 
Meirav Amram, Mina Teicher and Fei Ye
math.AG math.CO