Advertisement

manuscripta mathematica

, Volume 39, Issue 2–3, pp 253–262 | Cite as

The embedding dimension of the formal moduli space of certain curve singularities

  • Bernd Ulrich
Article

Abstract

For curve singularities which can be deformed into complete intersections the vector space dimension of T1 is estimated. Thus in the case that T2 is trivial we prove a formula of Deligne on the dimension of smoothing components with purely local methods.

Keywords

Exact Sequence Prime Ideal Complete Intersection Local Method Short Exact Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    BASSEIN, R.: On Smoothable Curve Singularities: Local Methods. Math. Ann.230, 273–277 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    BERGER, R.: Differentialmoduln eindimensionaler lokaler Ringe. Math. Z.81, 326–354 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    BUCHWEITZ, R.-O.: On Zariski's Criterion for Equisingularity and Non-Smoothable Monomial Curves. Thése de Doctorat d'Etat, Paris 1981Google Scholar
  4. [4]
    DELIGNE, P.: Intersections sur les surfaces régulières. Exposé X in: P. Deligne, N. Katz: Groupes de Monodromie en Géométrie Algébrique, SGA 7 II. Lecture Notes in Mathematics340, Springer-Verlag (1973)Google Scholar
  5. [5]
    GREUEL, G.-M.: On Deformation of Curves and a Formula of Deligne. To appear in: Proceedings of the International Conference on Algebraic Geometry, La Rabida (Spain), 1981Google Scholar
  6. [6]
    HERZOG, J.: Ein Cohen-Macaulay-Kriterium mit Anwendungen auf den Konormalenmodul und den Differentialmodul. Math. Z.163, 149–163 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    HERZOG, J.: Deformationen von Cohen-Macaulay Algebren. J. reine angew. Math.318, 83–105 (1980)MathSciNetzbMATHGoogle Scholar
  8. [8]
    HERZOG, J., KUNZ, E.: Der kanonische Modul eines CohenMacaulay-Rings. Lecture Notes in Mathematics238, Springer-Verlag (1971)Google Scholar
  9. [9]
    KOCH, J.: Über die Torsion des Differentialmoduls. Dissertation, Regensburg 1982Google Scholar
  10. [10]
    KUNZ, E.: Differentialformen auf algebraischen Varietäten mit Singularitäten II. Abh. math. Sem. Univ. Hamburg47, 42–70 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    KUNZ, E.: Series of talks at Purdue University during January and February 1982Google Scholar
  12. [12]
    PINKHAM, H.: Deformations of Algebraic Varieties with Gm Action. Asterisque20, 1–131 (1974)zbMATHGoogle Scholar
  13. [13]
    SCHEJA, G., STORCH, U.: Spurfunktionen bei vollständigen Durchschnitten. J. reine angew. Math.278/279, 174–190 (1975)zbMATHGoogle Scholar
  14. [14]
    STORCH, U.: Zur Längenberechnung von Moduln. Arch. Math.24, 39–43 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    ULRICH, B.: Torsion des Differentialmoduls und Kotangentenmodul von Kurvensingularitäten. Arch. Math.36, 510–523 (1981)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Bernd Ulrich
    • 1
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

Personalised recommendations