Skip to main content
SpringerLink
Log in

Regularity of ideals and their radicals

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

In this paper we compare the regularityreg I of a homogeneous idealI⊂K[x 1,...,x n] with that of its radical. We prove that regI ≥ reg\(\sqrt I\) ifR/I is a BuchsbaumR-module or ifI is a monomial ideal. We also prove the same result when\(\sqrt I\) defines a non-singular curve inP 3 under some additional hypotheses

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • [B] Bayer, D.: The Division Algorithm and the Hilbert Scheme. Ph.D. Thesis, Harvard University, 1982

  • [B-St] Bayer, D., Stillman, M.: A criterion for detectingm-regularity. Invent. Math. S7, 1–11 (1987)

    Article  MathSciNet  Google Scholar 

  • [D] D'Almeida, J.: Une properiété des courbes tracées sur une surface de degré inférieur ou égal à trois. C.R. Math. Ac. Sc.8, no. 3, 203–207 (1986)

    MATH  MathSciNet  Google Scholar 

  • [D-E-P] De Concini, C., Eisenbud, D., Procesi, P.: Hodge Algebras. Astérisque91 (1982)

  • [F-V] Eisenbud, D., Van de Ven, A.: On the normal bundle of smooth rational space curves. Math. Ann.256, 453–463 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  • [G] Gotzmann, G.: Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes. Math. Zeitschrift,158, 61–70 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  • [GLP] Gruson, L., Lazarsfeld, R., Peskine, G.: On a theorem of Castelnuovo, and the equations defining space curves. Invent. Math.72, 491–506 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  • [Gu] Gunning, R.:Lectures on Vector Bundles over Riemann Surfaces, Princeton University Press, 1967

  • [Ha] Hartshorne, R.:Algebraic Geometry, Graduate Texts in Mathematics,52, Springer-Verlag, 1977

  • [H-S] Hulek, K., Sacchiero, G.: On the normal bundls of elliptic space curves. Arch. Math.,40, 61–68 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  • [M-M] Möller, H.M., Mora, F.: New Constructive Methods in Classical Ideal Theory. Journal of Algebra100, 138–178 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • [Sch] Schreyer, F. O.: Diplomarbeit am Fachbereich Mathematik der Universität Hamburg, 1980

  • [Spe] Spear, D.: A constructive approach to commutative ring thory, Proceedings of the 1977 MACSYMA user's conference, NASA CP-2012 (1977)

  • [S-V1] Stückrad, J, Vogel, W.:Buchsbaum Rings and Applications, Springer-Verlag, 1986

  • [S-V2] Stückrad, J., Vogel, W.: Castelnuovo bounds for certain subvarieties inP n. Math. Ann.276, 341–352 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  • [Z] Zacharias, G.: Bachelor's thesis, M.I.T., 1978

Download references

Author information

Authors and Affiliations

  1. University of Sothern California, 90089, Los Angeles, CA

    M. S. Ravi

Authors
  1. M. S. Ravi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ravi, M.S. Regularity of ideals and their radicals. Manuscripta Math 68, 77–87 (1990). https://doi.org/10.1007/BF02568752

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02568752

Keywords

Search

Navigation