Quadratic vanishing cycles, reduction curves and reduction of the monodromy group of plane curve singularities

Abstract

The geometric monodromy of a plane curve singularity is a quasi-finite diffeomorphism. In this paper we locate the reduction curves of the geometric monodromy and the quadratic vanishing cycles of the singularity. An application to the geometric monodromy group is given.

20 pages, 16 figures