The Lefschetz property for families of curves
  By the Lefschetz hyperplane theorem, if X is a smooth quasi-projective variety and C a general curve section of X then the fundamental group of C surjects onto the fundamental group of X. Here we consider when this conclusion holds for a general member of an arbitrary family of curves that covers X. The most interesting case is families of rational curves. 
J\'anos Koll\'ar (Princeton Univ)
math.AG