I would like to know what is the second homology of a del Pezzo surface (X), that is blow-ups of \mathbb{CP}^2 in up to 9 points, and to be more precise what are the dimensions of the positive and negative definite subspaces. I.e. for the second Betti number b_2(X) what is b_+(X) and b_{-}(X) such that b_2(X) = b_+(X) + b_-(X).
In other words I want to know the full information of the intersection form Q of these surfaces.
I have tried to find information online and I was not successful in finding it. I would assume that such information are classified or listed somewhere. Any reference would help.
