Codimension 3 Arithmetically Gorenstein Subschemes of projective $N$-space

R. Hartshorne; I. Sabadini; E. Schlesinger

Codimension 3 Arithmetically Gorenstein Subschemes of projective $N$-space

Algebraic Geometry 2010-03-30 v2

Authors: R. Hartshorne , I. Sabadini , E. Schlesinger

Abstract

We study the lowest dimensional open case of the question whether every arithmetically Cohen--Macaulay subscheme of $\mathbb{P}^N$ is glicci, that is, whether every zero-scheme in $\mathbb{P}^3$ is glicci. We show that a set of $n \geq 56$ points in general position in $\PP^3$ admits no strictly descending Gorenstein liaison or biliaison. In order to prove this theorem, we establish a number of important results about arithmetically Gorenstein zero-schemes in $\mathbb{P}^3$ .

Keywords

arithmetically gorenstein subschemes projective space glicci cohen-macaulay liaison zero-schemes

Cite

@article{arxiv.math/0611478,
  title  = {Codimension 3 Arithmetically Gorenstein Subschemes of projective $N$-space},
  author = {R. Hartshorne and I. Sabadini and E. Schlesinger},
  journal= {arXiv preprint arXiv:math/0611478},
  year   = {2010}
}

Comments

to appear in Annales de l'Institut Fourier

Codimension 3 Arithmetically Gorenstein Subschemes of projective $N$-space

Abstract

Keywords

Cite

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