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Newton polyhedra and order of contact on real hypersurfaces

机译:Newton Polyhedra和真实过度迹象的联系人

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摘要

The purpose of this paper is to investigate order of contact on real hypersurfaces in 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.
机译:本文的目的是通过使用Newton Polyhedra在C〜N中的实际超缺陷的接触顺序,这是奇异性理论研究中的重要观念。更精确地,通过使用针对各个超细的定义功能的牛顿多面体给出了规则类型和奇异类型的平等的等效条件。此外,还给出了这种情况的足够条件,其更有用。许多早期已知的情况(凸形域,伪型x Reinhardt域和伪类型为4等)的凸形域,伪种条件是满足的。在上述条件下,可以从牛顿多面体的简单几何信息中直接看到类型的值。

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