Graded Betti numbers of Ideals of Fat Points
I(Z) = Ideal of fat point scheme Z supported at n general points of P2
Write down graded Betti numbers of minimal free resolution
0 → F1 → F0 → I(Z) → 0
of the ideal I(Z) for Z = m1p1 + ... + mnpn
for general points pi of the plane.
To run examples on your own computer, click here to obtain the Macaulay script used.
Note: The result is correct when the number of points is at most 8.
The result may be only conjectural for more than 8 points, assuming when
necessary the SHGH Conjecture and the Omega Conjecture.
This version is taciturn:
This version is verbose: