New cases of logarithmic equivalence of Welschinger and Gromov-Witten   invariants
  We consider the product of two projective lines equipped with the complex conjugation transforming $(x,y)$ into $(\bar{y},\bar{x})$ and blown up in at most two real, or two complex conjugate, points. For these four surfaces we prove the logarithmic equivalence of Welschinger and Gromov-Witten invariants. 
Ilia Itenberg, Viatcheslav Kharlamov, and Eugenii Shustin