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Biliaisons élémentaires en codimension 2

Mireille Martin-Deschamps (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Un théorème de Strano montre que si une courbe gauche localement Cohen-Macaulay n’est pas minimale dans sa classe de biliaison, elle admet une biliaison élémentaire strictement décroissante. R. Hartshorne a récemment donné une nouvelle preuve de ce résultat en le plaçant dans un contexte plus général. Dans cet article on apporte une précision, en utilisant les techniques introduites par Hartshorne : on montre que si un sous-schéma de codimension 2 localement Cohen-Macaulay de ℙ N n’est pas minimal...

Bornes pour la régularité de Castelnuovo-Mumford des schémas non lisses

Amadou Lamine Fall (2009)

Annales de l’institut Fourier

Nous montrons dans cet article des bornes pour la régularité de Castelnuovo-Mumford d’un schéma admettant des singularités, en fonction des degrés des équations définissant le schéma, de sa dimension et de la dimension de son lieu singulier. Dans le cas où les singularités sont isolées, nous améliorons la borne fournie par Chardin et Ulrich et dans le cas général, nous établissons une borne doublement exponentielle en la dimension du lieu singulier.

Codimension 3 Arithmetically Gorenstein Subschemes of projective N -space

Robin Hartshorne, Irene Sabadini, Enrico Schlesinger (2008)

Annales de l’institut Fourier

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 .

Geometry of arithmetically Gorenstein curves in P4.

Robin Hartshorne (2004)

Collectanea Mathematica

We characterize the postulation character of arithmetically Gorenstein curves in P4. We give conditions under which the curve can be realized in the form mH - K on some ACM surface. Finally, we complement a theorem by Watanabe by showing that any general arithmetically Gorenstein curve in P4 with arbitrary fixed postulation character can be obtained from a line by a series of ascending complete-intersection biliaisons.

Gorenstein liaison of some curves in P4.

Joshua Lesperance (2001)

Collectanea Mathematica

Despite the recent advances made in Gorenstein liaison, there are still many open questions for the theory in codimension ≥ 3. In particular we consider the following question: given two curves in Pn with isomorphic deficiency modules (up to shift), can they be evenly Gorenstein linked? The answer for this is yes for curves in P3, due to Rao, but for higher codimension the answer is not known. This paper will look at large classes of curves in P4 with isomorphic deficiency modules and show that...

On curves with natural cohomology and their deficiency modules

Giorgio Bolondi, Jean-Claude Migliore (1993)

Annales de l'institut Fourier

The minimal free resolution of the Hartshorne-Rao module of a curve with natural cohomology is studied, and conditions are given on the degrees and the ranks of the terms of this resolution.

On some properties of partial intersection schemes.

Alfio Ragusa, Giuseppe Zappalà (2003)

Collectanea Mathematica

Partial intersection subschemes of Pr of codimension c were used to furnish various graded Betti numbers which agree with a fixed Hilbert function. Here we study some further properties of such schemes; in particular, we show that they are not in general licci and we give a large class of them which are licci. Moreover, we show that all partial intersections are glicci. We also show that for partial intersections the first and the last Betti numbers, say m and p respectively, give bounds each other;...

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