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

M. V. Catalisano; A. Gimigliano

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

alg-geom 2008-02-03 v1 Algebraic Geometry

Authors: M. V. Catalisano , A. Gimigliano

Abstract

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 $Z$ .

Keywords

hilbert scheme hilbert functions rational points on curves

Cite

@article{arxiv.alg-geom/9412016,
  title  = {On the Hilbert Function of Fat Points on a Rational Normal Cubic},
  author = {M. V. Catalisano and A. Gimigliano},
  journal= {arXiv preprint arXiv:alg-geom/9412016},
  year   = {2008}
}

Comments

20 pages, plain TEX, no figures

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