Abstract Let (X, 0) ⊂ (ℂn, 0) be an irreducible weighted homogeneous singularity curve and let f : (X, 0) → (ℂ2, 0) be a finite map germ, one-to-one and weighted homogeneous with the same weights of (X, 0). We show that 𝒜e-codim(X, f) = μI(f), where the 𝒜e-codimension 𝒜e-codim(X, f) is the minimum number of parameters in a versal deformation and μI(f) is the image Milnor number, i.e. the number of vanishing cycles in the image of a stabilization of f.

中文翻译：

---

加权齐次不可约曲线之间映射的图像米尔诺数和𝒜e-codimension

摘要 令 (X, 0) ⊂ (ℂn, 0) 为不可约加权齐次奇点曲线，令 f : (X, 0) → (ℂ2, 0) 为有限映射胚，一对一且加权齐次(X, 0) 的权重相同。我们表明𝒜e-codim(X, f) = μI(f)，其中𝒜e-codimension 𝒜e-codim(X, f) 是通用变形中的最小参数数量，μI(f) 是图像的米尔诺数，即 f 的稳定图像中的消失循环数。