Global topology of images of finite complex analytic maps

Abstract

Let f[ratio ]X→[Copf]ℙ^p be a finite complex analytic map into complex projective space, with dimX<p. We obtain a result on the equivalence of low homotopy groups between the image of f and [Copf]ℙ^p, the level of comparison is a function of p, the maximal number of preimages of f and how bad the singularities of X are. This global result is deduced from a generalisation of a theorem of H. Hamm on the local structure of singularities, see [7].