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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Brieskorn, E. Die monodromie der isolierten singularitäten von hyperflächen. Manuscripta Math 2, 103–161 (1970). https://doi.org/10.1007/BF01155695
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DOI: https://doi.org/10.1007/BF01155695