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Asymptotic Behaviour of the Castelnuovo-Mumford Regularity

Published online by Cambridge University Press:  04 December 2007

S. DALE CUTKOSKY ,
JÜRGEN HERZOG  and
NGÔ VIÊT TRUNG
S. DALE CUTKOSKY
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA
JÜRGEN HERZOG
Affiliation:
Fachbereich Mathematik, Universität-GHS Essen, Postfach 103764, Germany; e-mail: mat300@uni-essen.de
NGÔ VIÊT TRUNG
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA
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Abstract

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In this paper the asymptotic behavior of the Castelnuovo$ndash;Mumford regularity of powers of a homogeneous ideal I is studied. It is shown that there is a linear bound for the regularity of the powers I whose slope is the maximum degree of a homogeneous generator of I, and that the regularity of I is a linear function for large n. Similar results hold for the integral closures of the powers of I. On the other hand we give examples of ideal for which the regularity of the saturated powers is asymptotically not a linear function, not even a linear function with periodic coefficients.

Keywords

Regularitypowers of idealssaturated powersRees algebra.
Type
Research Article
Information
Compositio Mathematica , Volume 118 , Issue 3 , September 1999 , pp. 243 - 261
Copyright
© 1999 Kluwer Academic Publishers