Ample divisors on the blow up of P at points

In this note we will prove a theorem on divisors on the blow up of P at points which extends a theorem of G. Xu [Xu] on the blow up of P. The central idea of the proof works for any dimension and therefore opens the doors to a generalization of the theorem to higher dimension, once one overcomes certain technical difficulties that arise. Basically we will give a new proof of Xu’s theorem that works also for P and so in most of this note n will be either 2 or 3.