We study the lowest dimensional open case of the question whether every arithmetically Cohen–Macaulay subscheme of is glicci, that is, whether every zero-scheme in is glicci. We show that a general set of points in 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 .
Nous étudions le problème de savoir si tous les sous-schémas arithmétiquement de Cohen-Macaulay de sont “glicci” dans le cas de plus petite dimension, c’est-à-dire le cas de sous-schémas de dimension zéro de . Nous prouvons qu’il n’y a pas de liaisons ni de biliaisons de Gorenstein descendantes d’un ensemble d’au moins 56 points généraux de . Pour démontrer ce théorème, nous établissons plusieurs résultats concernant les sous-schémas arithmétiquement de Gorenstein de .
Keywords: Gorenstein liaison, zero-dimensional schemes, $h$-vector
Mot clés : liaison de Gorenstein, schéma de dimension zéro, vecteur $h$
@article{AIF_2008__58_6_2037_0, author = {Hartshorne, Robin and Sabadini, Irene and Schlesinger, Enrico}, title = {Codimension $3$ {Arithmetically} {Gorenstein} {Subschemes} of projective $N$-space}, journal = {Annales de l'Institut Fourier}, pages = {2037--2073}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {6}, year = {2008}, doi = {10.5802/aif.2405}, zbl = {1155.14005}, mrnumber = {2473628}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2405/} }
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 SP - 2037 EP - 2073 VL - 58 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2405/ DO - 10.5802/aif.2405 LA - en ID - AIF_2008__58_6_2037_0 ER -
%0 Journal Article %A Hartshorne, Robin %A Sabadini, Irene %A Schlesinger, Enrico %T Codimension $3$ Arithmetically Gorenstein Subschemes of projective $N$-space %J Annales de l'Institut Fourier %D 2008 %P 2037-2073 %V 58 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2405/ %R 10.5802/aif.2405 %G en %F AIF_2008__58_6_2037_0
Hartshorne, Robin; Sabadini, Irene; Schlesinger, Enrico. Codimension $3$ Arithmetically Gorenstein Subschemes of projective $N$-space. Annales de l'Institut Fourier, Volume 58 (2008) no. 6, pp. 2037-2073. doi : 10.5802/aif.2405. http://archive.numdam.org/articles/10.5802/aif.2405/
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