Hilbert functions and resolutions for ideals of n = s^2 fat points in P2

Details Hilbert functions and resolutions for ideals of n = s^2 fat points in P2 Hilbert functions and resolutions for ideals of n = s^2 fat points in P2

2001-04-26

arxiv.org/abs/math/0104254v1

Mathematics

Algebraic Geometry

10 pages, 4 color postscript graphics

Scientific paper

Conjectures for the Hilbert function of the m-th symbolic power of the ideal of n general points of P2 are verified for infinitely many m for each square n > 9, using an approach developed by the authors in a previous paper. In those cases that n is even, conjectures for the resolution are also verified. Previously, by work of Evain (for the Hilbert function) and of Harbourne, Holay and Fitchett (for the resolution), these conjectures were known for infinitely many m for a given n > 9 only for n being a power of 4.

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