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Let ( X , 0) ⊂ (ℂ  n  , 0) be an irreducible weighted homogeneous singularity curve and let  f  : ( X , 0) → (ℂ 2 , 0) be a finite map germ, one-to-one and weighted homogeneous with the same weights of ( X , 0). We show that   e  -codim( X ,  f ) =  μ I  ( f ), where the   e  -codimension   e  -codim( X ,  f ) is the minimum number of parameters in a versal deformation and  μ I  ( f ) is the image Milnor number, i.e. the number of vanishing cycles in the image of a stabilization of  f .

Image Milnor number and 𝒜 e -codimension for maps between weighted homogeneous irreducible curves