Abstract
Let {f=0} be a hypersurface inC n+1 with a 1-dimensional singular set Σ. We consider the series of hypersurfaces {f+ɛx N=0} wherex is a generic linear form.
We derive a formula, which relates the characteristic polynomials of the monodromies off andf+ɛx N. Other ingredients in this formula are the horizontal and the vertical monodromies of the transversal (isolated) singularities on each branch of the singular set. We use polar curves and the carrousel method in the proof.
The formula is a generalization of the Iomdin formula for the Milnor numbers: µ(f+ɛx N)=µ n (f)−µ n −1(f)+Ne 0(Σ)
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Siersma, D. The monodromy of a series of hypersurface singularities. Commentarii Mathematici Helvetici 65, 181–197 (1990). https://doi.org/10.1007/BF02566602
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DOI: https://doi.org/10.1007/BF02566602