Codimension 3 Arithmetically Gorenstein Subschemes of projective N-space
[Sous-schémas arithmétiquement de Gorenstein de codimension 3 de l’espace projectif P N ]
Hartshorne, Robin ; Sabadini, Irene ; Schlesinger, Enrico
Annales de l'Institut Fourier, Tome 58 (2008), p. 2037-2073 / Harvested from Numdam
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Nous étudions le problème de savoir si tous les sous-schémas arithmétiquement de Cohen-Macaulay de ℙ N sont “glicci” dans le cas de plus petite dimension, c’est-à-dire le cas de sous-schémas de dimension zéro de ℙ 3 . 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 ℙ 3 . Pour démontrer ce théorème, nous établissons plusieurs résultats concernant les sous-schémas arithmétiquement de Gorenstein de ℙ 3 .

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 .

Publié le : 2008-01-01
DOI : https://doi.org/10.5802/aif.2405
Classification:  14C20,  14H50,  14M06,  14M07
Mots clés: liaison de Gorenstein, schéma de dimension zéro, vecteur h 
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     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},
     volume = {58},
     year = {2008},
     pages = {2037-2073},
     doi = {10.5802/aif.2405},
     zbl = {1155.14005},
     mrnumber = {2473628},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2008__58_6_2037_0}
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Hartshorne, Robin; Sabadini, Irene; Schlesinger, Enrico. Codimension $3$ Arithmetically Gorenstein Subschemes of projective $N$-space. Annales de l'Institut Fourier, Tome 58 (2008) pp. 2037-2073. doi : 10.5802/aif.2405. http://gdmltest.u-ga.fr/item/AIF_2008__58_6_2037_0/

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