Skip to main content

The divisor class group of ordinary and symbolic blow-ups

This is a preview of subscription content, access via your institution.


  1. Barshay, J.: Graded algebras of powers of ideals generated by A-sequences. J. Algebra25, 90–99 (1973)

    Google Scholar 

  2. Bourbaki, N.: Algèbra Commutative, Chapitre 2: Localization. Paris: Hermann 1961

    Google Scholar 

  3. Bourbaki, N.: Algèbra Commutative, Chapitre 7: Diviseurs. Paris: Hermann 1965

    Google Scholar 

  4. Bruns, W.: Die Divisorenklassengruppe der Restklassenringe von Polynomringen nach Determinantenidealen. Rev. Roum. Math. Pures Appl.20, 1109–1111 (1975)

    Google Scholar 

  5. Bruns, W.: The canonical module of a determinantal ring. Commutative Algebra: Durham, London Math. Soc. Lecture Notes72, 109–120 (1981)

    Google Scholar 

  6. Brodmann, M.: Blow-up and asymptotic depth of higher conormal modules. Preprint

  7. Bruns, W., Simis, A.: Symmetric algebras of modules arising from a fixed submatrix of a generic matrix. J. Pure Appl. Algebra,49, 227–245 (1987)

    Google Scholar 

  8. Fossum, R.: The divisor class group of a Krull domain, Ergebnisse der Mathematik, Band 74. Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  9. Goto, S.: The divisor class group of a certain Krull domain. J. Math. Kyoto Univ.17, 47–50 (1977)

    Google Scholar 

  10. Huneke, C.: On the finite generation of symbolic blow-ups. Math. Zeit.179, 465–472 (1982)

    Google Scholar 

  11. Huneke, C., Simis, A., Vasconcelos, W.: Reduced normal cones are domains Contemp. Math., to appear

  12. Herzog, J., Simis, A., Vasconcelos, W.: On the canonical module of the Rees algebra and the associated graded ring of an ideal. J. Algebra,105, 285–302 (1987)

    Google Scholar 

  13. Herzog, J., Vasconcelos, W.: On the divisor class group of Rees algebras. J. Algebra93, 182–188 (1985)

    Google Scholar 

  14. Katz, D., Ratliff, L.J., Jr.: On the symbolic Rees ring of a primary ideal. Commun. Algebra14, 959–970 (1986)

    Google Scholar 

  15. Rossi, M.E.: A note on symmetric algebras which are Gorenstein rings. Commun. Algebra11 (22) 2575–2591 (1983)

    Google Scholar 

  16. Samuel, P.: Lecture on Unique Factorization Domains (Notes by P. Murthy) Tata Inst. for Fund. Research, No. 30, Bombay 1964

  17. Shimoda, Y.: The class group of the Rees algebra over polynomial rings. Tokyo J. Math.2, 129–132 (1979)

    Google Scholar 

  18. Simis, A.: The basic exact sequence for the divisor class group of a normal Rees algebra (unpublished)

  19. Villarreal, R.: Koszul homology of Cohen-Macaulay ideals. Ph. D. thesis, Rutgers University

  20. Trung, N.V.: Über die Übertragung der Ringeigenschaften zwischenR undR[u]/(F). Math. Nachr.92, 215–229 (1979)

    Google Scholar 

Download references

Author information

Authors and Affiliations


Additional information

Partially supported by aCNP q grant

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Simis, A., Trung, N.V. The divisor class group of ordinary and symbolic blow-ups. Math Z 198, 479–491 (1988).

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI:


  • Class Group
  • Divisor Class
  • Divisor Class Group