Fundamental groups of algebraic fiber spaces

  • I. Shimada

    Hokkaido University, Sapporo, Japan


Let f:EBf: E\to B be a dominant morphism, where E and B are smooth irreducible complex quasi-projective varieties. Suppose that the general fiber F\sbbF\sb b of ff is connected. We present an algebro-geometric condition under which the boundary homomorphism :π2(B)π1(Fb)\partial : \pi_ 2 (B)\to \pi_1 (F_b) is well-defined, and makes the sequence

π2(B)π1(F\sbb)π1(E)π1(B)1\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