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On multiplicities of local rings

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Abstract

The aim of this note is to study multiplicities of local rings under (iterated) hyperplane sections, and Bezout-type theorems. An important application is a local version of a converse to Bezout's theorem. Even in the projective case this improves known results for arithmetically Cohen-Macaulay schemes. For the proofs our key result is a description of the behaviour of the Hilbert-Samuel polynomial in a short exact sequence. Using a generalization of this to the case of complexes we are also able to give an extended version of a theorem of Auslander-Buchsbaum and Serre expressing multiplicities by using Koszul-homology.

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Authors and Affiliations

  1. Mathematisches Institut der Universität, Bunsenstraße 3/5, D-W-3400, Göttingen, Federal Republic of Germany

    Hubert Flenner & Wolfgang Vogel

  2. FB Mathematik und Informatik der Universität, Postfach, D-O-4010, Halle, Federal Republic of Germany

    Wolfgang Vogel

Authors
  1. Hubert Flenner
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  2. Wolfgang Vogel
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Flenner, H., Vogel, W. On multiplicities of local rings. Manuscripta Math 78, 85–97 (1993). https://doi.org/10.1007/BF02599302

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