manuscripta mathematica

, Volume 43, Issue 2–3, pp 219–228

A criterion for tangential flatness

  • Bernd Herzog
Article

Abstract

We prove that a local homomorphism induces a flat homomorphism of the graduations with respect to the maximal ideals iff it is flat itself and the tangent cone of the fiber is just the fiber of the tangent cone mapping. More explicit, the statement we want to prove here is as follows.

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References

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    Grothendieck, A., Dieudonné, J.A.: Elements de Géométrie Algébrique, Berlin-Heidelberg-New York, Springer 1971Google Scholar
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    Herrmann, M., Orbanz, U.: Two notes on flatness, manuscripta math.40, 109–133 (1982)Google Scholar
  3. [3]
    Hersog, B.: Die Struktur flacher lokaler Erweiterungen lokaler Ringe, Beiträge Algebra Geom.11, 81–94 (1981)Google Scholar
  4. [4]
    Herzog, B.: Fibers of local homomorphisms such that flatness implies graduational flatness II, Forschungs ergebnisse Friedr,-Schiller-Univ. Jena N/81/49Google Scholar
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    Herzog, B,: On a relation between the Hilbert functions belonging to a local homomorphism, J. London Math. Soc.25, 458–466 (1982)Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Bernd Herzog
    • 1
  1. 1.Sektion MathematikFriedrich-Schiller-UniversitätJenaDDR

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