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January, 2021 Newton polyhedra and order of contact on real hypersurfaces
Joe KAMIMOTO
J. Math. Soc. Japan 73(1): 1-39 (January, 2021). DOI: 10.2969/jmsj/80868086

Abstract

The purpose of this paper is to investigate order of contact on real hypersurfaces in $\mathbb{C}^n$ 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.

Funding Statement

This work was supported by JSPS KAKENHI Grant Numbers JP15K04932, JP15H02057.

Citation

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Joe KAMIMOTO. "Newton polyhedra and order of contact on real hypersurfaces." J. Math. Soc. Japan 73 (1) 1 - 39, January, 2021. https://doi.org/10.2969/jmsj/80868086

Information

Received: 8 July 2018; Revised: 4 August 2019; Published: January, 2021
First available in Project Euclid: 9 May 2020

Digital Object Identifier: 10.2969/jmsj/80868086

Subjects:
Primary: 32F18

Rights: Copyright © 2021 Mathematical Society of Japan

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Vol.73 • No. 1 • January, 2021
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