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Resolutions of Fat Point Ideals Involving Eight General Points of P2

✍ Scribed by Stephanie Fitchett; Brian Harbourne; Sandeep Holay

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 169 KB
Volume: 244
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8931

No coin nor oath required. For personal study only.

✦ Synopsis

The main result, Theorem 1, provides an algorithm for determining the minimal free resolution of fat point subschemes of P 2 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 Grobner bases, is very fast. Partial information is also öbtained in certain cases with n ) 8.

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