Plain Varieties
  Algebraic varieties which are locally isomorphic to open subsets of affine space will be called {\em plain}. Plain varieties are smooth and rational. The converse is true for curves and surfaces, and unknown in general. It is shown that plain varieties are stable under blowup in smooth centers. 
G\'abor Bodn\'ar, Herwig Hauser, Josef Schicho, Orlando Villamayor