Resolutions of fat point ideals involving eight general points of P-2

The main result, Theorem 1. provides an algorithm for determining the minim al free resolution of fat point subschemes of P-2 involving up to eight gen eral points of arbitrary multiplicities. The resolutions obtained hold for any algebraically closed field, independent of the characteristic. The algo rithm works by giving a formula in nice cases and a reduction to the nice c ases otherwise. The algorithm, which does not involve Grobner bases, is ver y fast. Partial information is also obtained in certain cases with n > 8. ( C) 2001 Academic Press.