Codimension 3 Arithmetically Gorenstein Subschemes of projective N -space

Robin Hartshorne[1]; Irene Sabadini[2]; Enrico Schlesinger[2]

  • [1] University of California Department of Mathematics Berkeley, California 94720–3840 (USA)
  • [2] Politecnico di Milano Dipartimento di Matematica Piazza Leonardo da Vinci 32 20133 Milano (Italia)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 6, page 2037-2073
  • ISSN: 0373-0956

Abstract

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We study the lowest dimensional open case of the question whether every arithmetically Cohen–Macaulay subscheme of ℙ N is glicci, that is, whether every zero-scheme in ℙ 3 is glicci. We show that a general set of n ≥ 56 points in ℙ 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 ℙ 3 .

How to cite

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Hartshorne, Robin, Sabadini, Irene, and Schlesinger, Enrico. "Codimension $3$ Arithmetically Gorenstein Subschemes of projective $N$-space." Annales de l’institut Fourier 58.6 (2008): 2037-2073. <http://eudml.org/doc/10369>.

@article{Hartshorne2008,
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 general set of $n \ge 56$ points in $\mathbb\{P\}^3$ 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 $\mathbb\{P\}^3$.},
affiliation = {University of California Department of Mathematics Berkeley, California 94720–3840 (USA); Politecnico di Milano Dipartimento di Matematica Piazza Leonardo da Vinci 32 20133 Milano (Italia); Politecnico di Milano Dipartimento di Matematica Piazza Leonardo da Vinci 32 20133 Milano (Italia)},
author = {Hartshorne, Robin, Sabadini, Irene, Schlesinger, Enrico},
journal = {Annales de l’institut Fourier},
keywords = {Gorenstein liaison; zero-dimensional schemes; $h$-vector; -vector; parametrization},
language = {eng},
number = {6},
pages = {2037-2073},
publisher = {Association des Annales de l’institut Fourier},
title = {Codimension $3$ Arithmetically Gorenstein Subschemes of projective $N$-space},
url = {http://eudml.org/doc/10369},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Hartshorne, Robin
AU - Sabadini, Irene
AU - Schlesinger, Enrico
TI - Codimension $3$ Arithmetically Gorenstein Subschemes of projective $N$-space
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 6
SP - 2037
EP - 2073
AB - 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 general set of $n \ge 56$ points in $\mathbb{P}^3$ 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 $\mathbb{P}^3$.
LA - eng
KW - Gorenstein liaison; zero-dimensional schemes; $h$-vector; -vector; parametrization
UR - http://eudml.org/doc/10369
ER -

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