On the postulation of [formula omitted] fat points in [formula omitted

Abstract

In connection with his counter-example to the fourteenth problem of Hilbert, Nagata formulated a conjecture concerning the postulation of r fat points of the same multiplicity in P 2 and proved it when r is a square. Iarrobino formulated a similar conjecture in P d . We prove Iarrobino's conjecture when r is a dth power. As a corollary, we obtain new counter-examples modeled on those by Nagata.