Effective divisor classes and blowings-up of P2
Jeffrey A. Rosoff · Pacific Journal of Mathematics · 1980
Let X n -> P 2 be the monoidal transformation of the (complex) projective plane centered at distinct points P u •••,?" of P 2 .We recall that the Nέron-Severi group of X n is freely generated by the divisor class [L] of the proper transform L of a line in P 2 and by the classes [£ ?] of the "exceptional" fibers E r over P& the intersection pairing is given by [L] 2 =l; [L].[£J = 0; [£>]•[£,] = -δ uj .