Partial Intersections and Graded Betti Numbers

Alfio Ragusa and Giuseppe Zappalà

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

Full text of the article:

• Compressed DVI file (32 kilobytes)
• Compressed PostScript file (104 kilobytes)
• PDF file (228 kilobytes)