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Extremal Betti Numbers and Applications to Monomial Ideals

✍ Scribed by Dave Bayer; Hara Charalambous; Sorin Popescu

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 163 KB
Volume: 221
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7970

No coin nor oath required. For personal study only.

✦ Synopsis

Let S = k x 1

x n be the polynomial ring in n variables over a field k, let M be a graded S-module, and let

be a minimal free resolution of M over S. As usual, we define the associated (graded) Betti numbers β i j = β i j M by the formula

* The first and third authors are grateful to the NSF for support during the preparation of this work. The second author is grateful to Columbia University for its hospitality during the preparation of this manuscript. 497

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