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

Nagel, Uwe

doi:10.1090/S0002-9947-04-03595-0

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

Trans. Amer. Math. Soc. 357 (2005), 3585-3603

DOI: https://doi.org/10.1090/S0002-9947-04-03595-0

Published electronically: October 28, 2004

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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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