Contractible curves on a rational surface
  In this paper we prove that if S is a smooth, irreducible, projective, rational, complex surface and D an effective, connected, reduced divisor on S, then the pair (S,D) is contractible if the log-Kodaira dimension of the pair is $-\infty$. More generally, we even prove that this contraction is possible without blowing up an assigned cluster of points on S. Using the theory of peeling, we are also able to give some information in the case D is not connected. 
Alberto Calabri and Ciro Ciliberto
math.AG