论文标题
在准同质功能的模量空间上
On the moduli space of quasi-homogeneous functions
论文作者
论文摘要
我们将$（\ Mathbb {C}^2,0）$的分析等效函数的分析等效性细菌与其Bi-Lipschitz等价类别相关联。我们表明，任何不变的（减少）准同质函数的连续家庭具有恒定的Henry-Parusiński不变性的不变性。此外，我们表明，在同一亨利·帕鲁斯基（Henry-Parusiński）不变的准均匀函数中，只有有限数量的不同的Bi-lipschitz类，提供了此数字的最大配额。
We relate the moduli space of analytic equivalent germs of reduced quasi-homogeneous functions at $(\mathbb{C}^2,0)$ with their bi-Lipschitz equivalence classes. We show that any non-degenerate continuous family of (reduced) quasi-homogeneous functions with constant Henry-Parusiński invariant is analytically trivial. Further we show that there are only a finite number of distinct bi-Lipschitz classes among quasi-homogeneous functions with the same Henry-Parusiński invariant providing a maximum quota for this number.
