On the Hilbert Function of Fat Points on a Rational Normal Cubic

Details On the Hilbert Function of Fat Points on a Rational Normal Cubic On the Hilbert Function of Fat Points on a Rational Normal Cubic

1994-12-15

arxiv.org/abs/alg-geom/9412016v1

Mathematics

Algebraic Geometry

20 pages, plain TEX, no figures

Scientific paper

In this paper we find an algorithm which computes the Hilbert function of schemes $Z$ of "fat points" in $\PP3$ whose support lies on a rational normal cubic curve $C$. The algorithm shows that the maximality of the Hilbert function in degree $t$ is related to the existence of fixed curves (either $C$ itself or one of its secant lines) for the linear system of surfaces of degree $t$ containing $Z$.

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