The monodromy of a series of hypersurface singularities

Dirk Siersma*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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 languageEnglish
Pages (from-to)181-197
Number of pages17
JournalCommentarii Mathematici Helvetici
Volume65
Issue number1
DOIs
Publication statusPublished - Dec 1990

Fingerprint

Dive into the research topics of 'The monodromy of a series of hypersurface singularities'. Together they form a unique fingerprint.

Cite this