Effective divisor classes and blowings-up of P²

Abstract

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 Nron-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