论文标题
牛顿多面体和实际超曲面上的接触顺序
Newton polyhedra and order of contact on real hypersurfaces
论文作者
论文摘要
本文的目的是通过使用Newton Polyhedra来研究$ {\ Mathbb C}^n $中真实Hypersurfaces的接触顺序，这在奇异理论研究中是重要的概念。更确切地说，通过使用相应超出表面的定义函数的牛顿多面体给出了常规类型和奇异类型平等的等效条件。此外，还给出了更有用的这种情况的足够条件。这种足够的条件得到了许多早期已知病例（凸域，pseudoconvex reinhardt域和普通类型为4等的pseudoconvex域）。在上述条件下，可以在牛顿多面体的简单几何信息中直接看到类型的值。
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.
