0 Ju n 20 05 Resolutions of ideals of six fat points in P 2
نویسندگان
چکیده
The graded Betti numbers of the minimal free resolution (and also therefore the Hilbert function) of the ideal of a fat point subscheme Z of P are determined whenever Z is supported at any 6 or fewer distinct points. We also handle a broad range of cases in which the points can be infinitely near, related to the classification of normal cubic surfaces. All results hold over an arbitrary algebraically closed field k.
منابع مشابه
Ideals of Six General Fat Points on the Projective Plane
Let X be the blowup of P 2 at six general points p 1 ; : : :; p 6 and let L X be the total transform of a line on P 2. We show that the natural multiplication map ? L)) has maximal rank for any numerically eeective divisor F on X. This fact implicitly allows determination of minimal free resolutions for ideals deening fat point subschemes Z = m 1 p 1 + + m 6 p 6 of P 2 .
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The main result, Theorem 1, provides an algorithm for determining the minimal free resolution of fat point subschemes of P involving up to 8 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 algorit...
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