# Fundamental groups of algebraic fiber spaces

### I. Shimada

Hokkaido University, Sapporo, Japan

## Abstract

Let $f:E→B$ be a dominant morphism, where E and B are smooth irreducible complex quasi-projective varieties. Suppose that the general fiber $F_{b}$ of $f$ is connected. We present an algebro-geometric condition under which the boundary homomorphism $∂:π_{2}(B)→π_{1}(F_{b})$ is well-defined, and makes the sequence

$π_{2}(B)→π_{1}(F_{b})→π_{1}(E)→π_{1}(B)→1$

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