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Two notes on flatness

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Abstract

The first note gives some characterization offlat morphisms by (generalized) Hilbert functions. The second note yields a geometric description of tangential flatness, i.e. the flatness of the induced morphism in the tangent cones. The appendix contains a graded version of the local criterion of flatness as well as some consequences which are used in the main part of the paper.

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References

  1. M. Herrmann - U. Orbanz, Faserdimensionen von Auf- blasungen lokaler Ringe und Äquimultiplizität, J. Math. Kyoto Univ. 20 (1980), 651–659

    Google Scholar 

  2. M. Herrmann - R. Schmidt - W. Vogel, Theorie der normalen Flachheit, Teubner-Verlag, Leipzig 1977

    Google Scholar 

  3. B. Herzog, Die Wirkung lokaler Homomorphismen auf die Hilbertfunktion, Math. Nachr. 97 (1980), 103–115

    Google Scholar 

  4. B. Herzog, On a relation between the Hilbert functions belonging to a local homomorphism, Forschungsergebnisse Friedrich-Schiller-Universität Jena 1981 (to appear in Bull. London Math. Soc.)

  5. B. Herzog, Fibres of local homomorphisms such that flatness implies graduational flatness, Forschungsergebnisse Friedrich-Schiller-Universität Jena 1981

  6. B. Herzog, Fibres of local homomorphisms such that flatness implies graduational flatness II, Forschungsergebnisse Friedrich-Schiller-Universität Jena 1981

  7. M. Höchster - L.J. Ratliff, Five theorems on Macaulay rings, Pacific J. Math. 44 (1973), 147–172

    Google Scholar 

  8. M. Lejeune, Contributions a l'étude des singularités du point de vue du polygone de Newton, These Paris 1973

  9. H. Matsumura, Commutative algebra, Benjamin, New York 1970

    Google Scholar 

  10. N.I. Shepherd-Barron, Local homomorphisms and Hilbert-Samuel functions, Bull. London Math. Soc. 11 (1979), 138–141

    Google Scholar 

  11. P. Valabrega - G. Valla, Form rings and regular sequences, Nagoya Math. J. 72 (1978), 93–101

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut der Universität zu Köln, Weyertal 86-90, D-5000, Köln 41

    Manfred Herrmann & Ulrich Orbanz

Authors
  1. Manfred Herrmann
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  2. Ulrich Orbanz
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Herrmann, M., Orbanz, U. Two notes on flatness. Manuscripta Math 40, 109–133 (1982). https://doi.org/10.1007/BF01168239

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  • DOI: https://doi.org/10.1007/BF01168239

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