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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.

Given an analytic function germ f : (X, 0) → C on an isolated determinantal singularity or on a reduced curve, we present formulas relating the local Euler obstruction of f to the vanishing Euler characteristic of the fiber X ∩ f −1 (0) and to the Milnor number of f . Restricting ourselves to the case where X is a complete intersection, we obtain an easy way to calculate the local Euler obstruction of f as the difference between the dimension of two algebras.

A theorem by D. Mond shows that if ∶ (ℂ, 0) → ( ℂ 2 , 0 ) is finite and has has degree one onto its image ( , 0), then the A -codimension is less than or equal to the image Milnor number ( ), with equality if and only if ( , 0) is weighted homogeneous.Here we generalize this result to the case of a map germ ∶ ( , 0), where ( , 0) is a plane curve singularity. K E Y W O R D SA -codimension, image Milnor number, curve singularities M S C ( 2 0 1 0 ) Primary: 32S30; Secondary: 32S05, 58K60

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