On the Monodromy at Isolated Singularities of Weighted Homogeneous Polynomials

Abstract

Then AT is (am -3)-connected, Hm_2(K) is the direct sum of a free abelian group of rank q + (-l)m and a cyclic group of order d/q, and Hm_x(K) is free abelian of rank q + (-l)m. I am grateful to Peter Orlik for the survey article [7] which brought the problem to my attention and which has a good bibliography on this and related subjects.1. Preliminaries. Let /: C" -* C be a polynomial, and let V = f~x(0). If V has a singularity at z0, that is, all the partial derivatives of/vanish there, let St denote the (2m -l)-sphere in C" of radius e, centered at z0, and write K = V n Se. Then for all e sufficiently small, the portion of V inside Se is homeomorphic to the cone over K [3, p. 18], and so we are interested in the topology of K.