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首页> 外文期刊>Journal of the Mathematical Society of Japan >Real Seifert form determines the spectrum for semiquasihomogeneous hypersurface singulartities in C~3
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Real Seifert form determines the spectrum for semiquasihomogeneous hypersurface singulartities in C~3

机译:实际的塞弗特形式决定了C〜3中半准超表面奇异性的频谱

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摘要

We show that the real Seifert form determines the weights for nondegenerate quasihomogeneous polynomials in C~3. Consequently the real Seifert form determines the spectrum for semiquasihomogeneous hypersurface Singularities in C~3. A a corollary, we obtain the topological invariance of Weights for nondegenerate quasihomogeneous polynomials in C~3. Which has Already been proved by the author [Sae1] and independently by Xu and Yau [Ya1], [Ya2], [XY1],[XY2]. The method in this paper is totally different from their approaches and gives some new results, as corollaries, about holomorphic function germs in C~3 which are connected by μ-constant deformations to nondegenerate quasihomogeneous polynomials. For example, we show that two seiquasihomogeneous functions of three complex variables have the same topological type if and only if they are connected by a μ-constant deformation.
机译:我们证明了真实的塞弗特形式决定了C〜3中非简并准多项式的权重。因此,真实的塞弗特形式决定了C〜3中半准超表面奇异点的光谱。一个推论,我们获得了C〜3中非简并拟齐次多项式的权重的拓扑不变性。这已经由作者[Sae1]证明,并且由Xu和Yau [Ya1],[Ya2],[XY1],[XY2]独立证明。本文中的方法与它们的方法完全不同,并作为推论,给出了C〜3中的全纯函数种的新结果,这些种通过μ常数变形与非退化拟齐次多项式联系在一起。例如,我们表明,当且仅当它们通过μ恒定变形连接时,三个复变量的两个准齐均函数具有相同的拓扑类型。

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