Abstract
The main result, Theorem 1, provides an algorithm for determining the minimal free resolution of fat point subschemes of P2 involving up to eight general points of arbitrary multiplicities. The resolutions obtained hold for any algebraically closed field, independent of the characteristic. The algorithm works by giving a formula in nice cases and a reduction to the nice cases otherwise. The algorithm, which does not involve Gröbner bases, is very fast. Partial information is also obtained in certain cases with n>8.
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