On Fundamental Groups of Fibered Complex Manifolds

摘要

Let X be a (not necessarily compact) complex manifold. A fibration on X is by definition a proper flat holomorphic map f: X → Y with connected fibers from X onto a complex manifold Y. A fiber f~(-1)(y) is called singular if y is a critical value of f and smooth otherwise. We denote by Sing f the locus of the points of X where f is not smooth. Remmert's proper mapping theorem implies that the set f(Sing f) of critical values of the fibration f: X → Y is a closed analytic subset of Y.