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Smallest Graded Betti Numbers

✍ Scribed by Benjamin P Richert

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 153 KB
Volume: 244
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8878

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✦ Synopsis

It is known that given a Hilbert function H H, there need not exist a module which has uniquely the smallest graded Betti numbers among all modules attaining H H. In this paper we extend the previous example of this behavior to an infinite family and demonstrate with a second infinite family that even when the given Hilbert function is that of a complete intersection, a module with uniquely smallest graded Betti numbers need not exist. Finally we prove a conjecture of Geramita, Harima, and Shin concerning the non-existence of uniquely smallest graded Betti numbers among all Gorenstein rings attaining a given Hilbert function.

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