On the Milnor fibre and Lê numbers of semiweighte

Authors: Michelle F Z Morgado Marcelo J Saia

Publish Date: 2012/11/10

Volume: 43, Issue: 4, Pages: 615-636

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Abstract

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemiweighted homogeneous polynomials of the same type which we call semiweighted homogeneous arrangements It is shown how the Lê numbers of such polynomials are computed using only their weights and degree of homogeneity A key point of the main theorem is to find the number called polar ratio of this polynomial class An important consequence is the description of the Euler characteristic of the Milnor fibre of such arrangements only depending on their weights and degree of homogeneityThe constancy of the Lê numbers in families formed by such arrangements is shown with the deformed terms having weighted degree greater than the weighted degree of the initial germ Moreover using the results of Massey applied to families of function germs we obtain the constancy of the homology of the Milnor fibre in this family of semiweighted homogeneous arrangements

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