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Compositio Mathematica

, Volume 118, Issue 3, pp 243–261 | Cite as

Asymptotic Behaviour of the Castelnuovo-Mumford Regularity

  • S. Dale Cutkosky
  • Jürgen Herzog
  • Ngô Viêt Trung
Article

Abstract

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.

Regularity powers of ideals saturated powers Rees algebra. 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • S. Dale Cutkosky
    • 1
  • Jürgen Herzog
    • 2
  • Ngô Viêt Trung
    • 3
  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Fachbereich MathematikUniversität-GHS EssenPostfachGermany; e-mail
  3. 3.Institute of MathematicsBo Ho, HanoiVietnam

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