Let f be an isolated singularity at the origin of $\mathbb {C}^n$. One of many invariants that can be associated with f is its Łojasiewicz exponent $\mathcal {L}_0 (f)$, which measures, to some extent, the topology of f. We give, for generic surface singularities f, an effective formula for $\mathcal {L}_0 (f)$ in terms of the Newton polyhedron of f. This is a realization of one of Arnold’s postulates.

中文翻译：

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非简并表面奇点的 Łojasiewicz 指数

设f为$\mathbb {C}^n$原点处的孤立奇点。与f相关的众多不变量之一是它的 Łojasiewicz 指数$\mathcal {L}_0 (f)$ ，它在某种程度上测量了f的拓扑。对于一般表面奇点f ，我们根据f的牛顿多面体给出$\mathcal {L}_0 (f)$ 的有效公式。这是阿诺德假设之一的实现。