The open Gromov-Witten-Welschinger theory of blowups of the projective   plane
  We compute the Welschinger invariants of blowups of the projective plane at an arbitrary conjugation invariant configuration of points. Specifically, open analogues of the WDVV equation and Kontsevich-Manin axioms lead to a recursive algorithm that reconstructs all the invariants from a small set of known invariants. Example computations are given, including the non-del Pezzo case. 
Asaf Horev, Jake P. Solomon
math.SG hep-th math.AG