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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Comparing Castelnuovo-Mumford regularity and extended degree: The borderline cases


Author: Uwe Nagel
Journal: Trans. Amer. Math. Soc. 357 (2005), 3585-3603
MSC (2000): Primary 13D40, 13D45; Secondary 13P10, 14M05
Published electronically: October 28, 2004
MathSciNet review: 2146640
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Abstract: Castelnuovo-Mumford regularity and any extended degree function can be thought of as complexity measures for the structure of finitely generated graded modules. A recent result of Doering, Gunston, and Vasconcelos shows that both can be compared in the case of a graded algebra. We extend this result to modules and analyze when the estimate is in fact an equality. A complete classification is obtained if we choose as extended degree the homological or the smallest extended degree. The corresponding algebras are characterized in three ways: by relations among the algebra generators, by using generic initial ideals, and by their Hilbert series.


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Additional Information

Uwe Nagel
Affiliation: Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, Kentucky 40506-0027
Email: uwenagel@ms.uky.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03595-0
PII: S 0002-9947(04)03595-0
Keywords: Castelnuovo-Mumford regularity, extended degree, generic initial ideal, Hilbert series, homological degree, smallest extended degree
Received by editor(s): April 2, 2003
Received by editor(s) in revised form: December 5, 2003
Published electronically: October 28, 2004
Article copyright: © Copyright 2004 American Mathematical Society