no. 6
Codimension 3 Arithmetically Gorenstein Subschemes of projective N-space
[Sous-schémas arithmétiquement de Gorenstein de codimension 3 de l’espace projectif P N ]
Hartshorne, Robin1 ; Sabadini, Irene2 ; Schlesinger, Enrico2
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, Tome 58 (2008) no. 6, pp. 2037-2073.

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 .

DOI : 10.5802/aif.2405
Classification : 14C20, 14H50, 14M06, 14M07
Keywords: Gorenstein liaison, zero-dimensional schemes, $h$-vector
Mot clés : liaison de Gorenstein, schéma de dimension zéro, vecteur $h$

Hartshorne, Robin 1 ; Sabadini, Irene 2 ; Schlesinger, Enrico 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) 
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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) no. 6, pp. 2037-2073. doi : 10.5802/aif.2405. https://aif.centre-mersenne.org/articles/10.5802/aif.2405/

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