Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 44, No. 1, pp. 285-302 (2003)

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Partial Intersections and Graded Betti Numbers

Alfio Ragusa and Giuseppe Zappalà

Dipartimento di Matematica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy, e-mail:; e-mail:

Abstract: It is well known that for $2$-codimensional aCM subschemes of ${\mathbb P}^r$ with a fixed Hilbert function $H$ there are all the possible graded Betti numbers between suitable bounds depending on $H.$ For aCM subschemes of codimension $c\ge 3$ with Hilbert function $H$ it is just known that there are upper bounds for the graded Betti numbers depending on $H$ and these can be reached; but what are the graded Betti numbers which can be realized is not yet completely understood. The aim of the paper is to construct $c$-codimensional subschemes of ${\mathbb P}^r$ which could recover as many graded Betti numbers as possible generalizing both the $2$-codimensional case and the maximal case.

Classification (MSC2000): 13D40, 13H10

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Electronic version published on: 3 Apr 2003. This page was last modified: 4 May 2006.

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