2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60748The main result provides an algorithm for determining the minimal free resolution of ideals of fat point subschemes of ${\bf P}^2$ involving up to 8 general points with arbitrary multiplicities; the results hold over algebraically closed fields of any characteristic. The algorithm, which works by giving a formula in certain cases and a reduction to these cases otherwise, does not involve Gröbner bases, and so is very fast, even for very large multiplicities. Partial information is also obtained in certain cases with $n>8$.12 pages PlainTeXAlgebraic GeometryCommutative Algebra13P10, 14C99text