# Fundamental groups of algebraic fiber spaces

### I. Shimada

Hokkaido University, Sapporo, Japan

## 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

$\pi_2 (B) \to \pi_1 (F\sb b) \to \pi_1 (E)\to \pi_1 (B) \to 1$

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

## Cite this article

I. Shimada, Fundamental groups of algebraic fiber spaces. Comment. Math. Helv. 78 (2003), no. 2, pp. 335–362

DOI 10.1007/S000140300014