Resolutions of fat point ideals involving 8 general points of P2

Details Resolutions of fat point ideals involving 8 general points of P2 Resolutions of fat point ideals involving 8 general points of P2

2001-01-12

arxiv.org/abs/math/0101110v1

Mathematics

Algebraic Geometry

12 pages PlainTeX

Scientific paper

The 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 Gr\"obner bases, and so is very fast, even for very large multiplicities. Partial information is also obtained in certain cases with $n>8$.

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