论文标题
布鲁斯·罗伯特（Bruce-Roberts
Bruce-Roberts Numbers and Quasihomogeneous Functions on Analytic Varieties
论文作者
论文摘要
考虑到分析品种的细菌$ x $和一个全体形函数$ f $的细菌，与$ x $的对数分层具有分层孤立的奇异性，我们表明，在某些条件下，对奇异性$ $ $（f，x）$的奇异性类型（f，x）$，以下是众所周知的K. saito的saito saito theorem的相对相对相对的相对数字：作为布鲁斯·罗伯特（Bruce-Roberts）的数字）相当于对$（f，x）$的相对准杂种性，即存在坐标系统，以至于$ f $ and $ x $都相对于相同的正理性权重。
Given a germ of an analytic variety $X$ and a germ of a holomorphic function $f$ with a stratified isolated singularity with respect to the logarithmic stratification of $X$, we show that under certain conditions on the singularity type of the pair $(f,X)$, the following relative analog of the well known K. Saito's theorem holds true: equality of the relative Milnor and Tjurina numbers of f with respect to X (also known as Bruce-Roberts numbers) is equivalent to the relative quasihomogeneity of the pair $(f,X)$, i.e. to the existence of a coordinate system such that both $f$ and $X$ are quasihomogeneous with respect to the same positive rational weights.
