Fundamental groups of algebraic fiber spaces

I. Shimada

doi:10.1007/s000140300014

JournalscmhVol. 78, No. 2pp. 335–362

Fundamental groups of algebraic fiber spaces

I. Shimada
Hokkaido University, Sapporo, Japan

Download PDF

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 $F_{b}$ of $f$ is connected. We present an algebro-geometric condition under which the boundary homomorphism $\partial : π_{2} (B) \to π_{1} (F_{b})$ is well-defined, and makes the sequence

π_{2} (B) \to π_{1} (F_{b}) \to π_{1} (E) \to π_{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