TY - JOUR

T1 - Newton polyhedra and order of contact on real hypersurfaces

AU - Kamimoto, Joe

N1 - Funding Information:
2010 Mathematics Subject Classification. Primary 32F18. Key Words and Phrases. singular type, regular type, finite type, order of contact, Newton polyhedra, nondegeneracy condition. This work was supported by JSPS KAKENHI Grant Numbers JP15K04932, JP15H02057.
Publisher Copyright:
© 2021 The Mathematical Society of Japan

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

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U2 - 10.2969/JMSJ/80868086

DO - 10.2969/JMSJ/80868086

M3 - Article

AN - SCOPUS:85101010107

VL - 73

SP - 1

EP - 39

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 1

ER -