Newton polyhedra and order of contact on real hypersurfaces

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    The purpose of this paper is to investigate order of contact on real hypersurfaces in Cn by using Newton polyhedra which are important notion in the study of singularity theory. To be more precise, an equivalence condition for the equality of regular type and singular type is given by using the Newton polyhedron of a defining function for the respective hypersurface. Furthermore, a sufficient condition for this condition, which is more useful, is also given. This sufficient condition is satisfied by many earlier known cases (convex domains, pseudoconvex Reinhardt domains and pseudoconvex domains whose regular types are 4, etc.). Under the above conditions, the values of the types can be directly seen in a simple geometrical information from the Newton polyhedron.

    Original languageEnglish
    Pages (from-to)1-39
    Number of pages39
    JournalJournal of the Mathematical Society of Japan
    Issue number1
    Publication statusPublished - 2021

    All Science Journal Classification (ASJC) codes

    • General Mathematics


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