ar X iv : m at h / 99 06 13 0 v 1 [ m at h . A G ] 1 8 Ju n 19 99 Resolutions of Ideals of Uniform Fat Point Subschemes of P 2 Brian

Let I be the ideal defining a set of general points p1, . . . , pn ∈ P2. There recently has been progress in showing that a naive lower bound for the Hilbert functions of symbolic powers I(m) is in fact attained when n > 9. Here, for m sufficiently large, the minimal free graded resolution of I(m) is determined when n > 9 is an even square, assuming only that this lower bound on the Hilbert function is attained. Under ostensibly stronger conditions (that are nonetheless expected always to hold), a similar result is shown to hold for odd squares, and for infinitely many m for each nonsquare n bigger than 9. All results hold for an arbitrary algebraically closed field k.