Abstract
Let {f=0} be a hypersurface in C n+1 with a 1-dimensional singular set Σ. We consider the series of hypersurfaces {f+e{open}x N=0} where x is a generic linear form. We derive a formula, which relates the characteristic polynomials of the monodromies of f and f+e{open}x 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+e{open}x N )=μ n (f)-μ n -1(f)+Ne 0(Σ)
Original language | English |
---|---|
Pages (from-to) | 181-197 |
Number of pages | 17 |
Journal | Commentarii Mathematici Helvetici |
Volume | 65 |
Issue number | 1 |
DOIs | |
Publication status | Published - Dec 1990 |