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Invariants of hypersurface singularities in positive characteristic

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Abstract

We study singularities f∈K[[x 1,…,x n ]] over an algebraically closed field K of arbitrary characteristic with respect to right respectively contact equivalence, and we establish that the finiteness of the Milnor respectively the Tjurina number is equivalent to finite determinacy. We give improved bounds for the degree of determinacy in positive characteristic. Moreover, we consider different non-degeneracy conditions of Kouchnirenko, Wall and Beelen-Pellikaan in positive characteristic, and we show that planar Newton non-degenerate singularities satisfy Milnor’s formula μ=2⋅δ−r+1. This implies the absence of wild vanishing cycles in the sense of Deligne.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Kaiserslautern, Erwin–Schrödinger–Straße, 67663, Kaiserslautern, Germany

    Yousra Boubakri, Gert-Martin Greuel & Thomas Markwig

Authors
  1. Yousra Boubakri
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  2. Gert-Martin Greuel
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  3. Thomas Markwig
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Correspondence to Gert-Martin Greuel.

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Boubakri, Y., Greuel, GM. & Markwig, T. Invariants of hypersurface singularities in positive characteristic. Rev Mat Complut 25, 61–85 (2012). https://doi.org/10.1007/s13163-010-0056-1

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  • DOI: https://doi.org/10.1007/s13163-010-0056-1

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