Image Milnor number and \mathscrA_e-codimension for maps between weighted homogeneous irreducible curves

2017/09/27 by Ament, Daiane Alice Henrique, Ballesteros, Juan Jose Nuño, Tomazella, João Nivaldo
#32S05 (Secondary) #32S30 (Primary) #58K60 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.09504

Abstract

Let (X,0)⊂ (ℂⁿ,0) be an irreducible weighted homogeneous singularity curve and let f:(X,0)→(ℂ²,0) be a map germ finite, one-to-one and weighted homogeneous with the same weights of (X,0). We show that \mathscrA_e-codim(X,f)=μ_I(f), where \mathscrA_e-codim(X,f) is the \mathscrA_e-codimension, i.e., 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 stabilisation of f.

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