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manuscripta mathematica

, Volume 2, Issue 2, pp 103–161 | Cite as

Die monodromie der isolierten singularitäten von hyperflächen

  • Egbert Brieskorn
Article

Abstract

J. Milnor recently introduced the local Picard-Lefschetz-monodromy of an isolated singularity of a hypersurface. This is an important tool in the investigation of the topology of singularities. The monodromy is an action on a certain cohomology group and is defined in topological terms. In this paper we find an algebraic description of the monodromy. We construct by algebraic methods a regular singular ordinary linear differential operator, such that the monodromy of this singular operator coincides with the Picard-Lefschetz monodromy. As an application we prove that the eigenvalues of the monodromy are roots of unity. Our treatment is close in spirit to Grothendiecks theory of the Gauβ-Manin-connection.

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Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • Egbert Brieskorn
    • 1
  1. 1.Mathematisches Institut der Universität Göttingen34 Göttingen

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