Fundamental groups of algebraic fiber spaces

Abstract

Let $f: E\to B$ be a dominant morphism, where E and B are smooth irreducible complex quasi-projective varieties. Suppose that the general fiber $F\sb b$ of $f$ is connected. We present an algebro-geometric condition under which the boundary homomorphism $\partial : \pi_ 2 (B)\to \pi_1 (F_b)$ is well-defined, and makes the sequence

exact. As an application, we calculate the fundamental group of the complement to the dual hypersurface of a smooth projective curve.