Abstract :
In this paper we determine a new upper bound for the regularity index of fat points of P2, without requiring any geometric condition on the points. This bound is intermediate between Segre′s bound, that holds for points in the general position, and the more general bound, that is attained when the points are collinear: in fact, both of these bounds can be recovered as particular cases. Furthermore, our bound cannot, in general, be sharpened: in fact, it is attained if there are either many collinear points or collinear points with high multiplicities.
