Mnev-Sturmfels universality for schemes
  We prove a scheme-theoretic version of Mnev-Sturmfels Universality, suitable to be used in the proof of Murphy's Law in Algebraic Geometry. Somewhat more precisely, we show that any singularity type of finite type over Z appears on some incidence scheme of points and lines, subject to some particular further constraints. 
Seok Hyeong Lee and Ravi Vakil
math.AG