Upper Bounds for the Regularity Index of Fat Points Original Research Article

In a recent paper the authors and M. V. Catalisano gave a sharp bound for the regularity index of fat points in general position in imagen, n ≥ 2. In this paper we shall see that. under some mild condition. This bound is attained if and only if the points lie on a rational normal curve, and that for fat points with the uniform position property there are other good bounds involving the regularity index and the Hilbert function of the given set of points.