c3中线性部为幂零的奇异向量场的约简形式

Pub Date : 2015-08-01 DOI:10.1619/FESI.58.253

M. Miyake

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引用次数: 1

摘要

研究了原点为幂零线性部分的全纯奇异向量场的约简问题，P = (y + a(X))偏导数(X) + (z + b(X))偏导数(y) + c(X)偏导数(z)，其中X = (X, y, z)是c -3中的一个元素。通过引入a . Shirai在上一篇论文[M-S]中给出的拟估值的概念，我们刻画了一类可以通过坐标的形式变换简化成更简单的类，这类类在定理a和定理B中允许有各种变化。

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Reduced Forms of a Singular Vector Field in C 3 with Nilpotent Linear Part

We study the reduction problem for a holomorphic singular vector field with nilpotent linear part at the origin, P = (y + a(X))partial derivative(x) + (z + b(X))partial derivative(y) + c(X)partial derivative(z), where X = (x, y, z) is an element of C-3. By introducing a notion of quasi-valuation, which was given in the previous paper [M-S] with A. Shirai, we characterize a class which can be reduced into simpler ones by formal change of coordinates which admit various variations in Theorems A and B.

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