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- Title
Fundamental groups of algebraic fiber spaces.
- Authors
I. Shimada
- Abstract
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 $F\sb b$</formula> of $f$ is connected. We present an algebro-geometric condition under which the boundary homomorphism $\partial : \pi_ 2 (B)\to \pi_1 (F_b)$</formula> is well-defined, and makes the sequence $$\pi_2 (B) \to \pi_1 (F\sb b) \to \pi_1 (E)\to \pi_1 (B) \to 1$$</formula> exact. As an application, we calculate the fundamental group of the complement to the dual hypersurface of a smooth projective curve.
- Subjects
HOMOMORPHISMS; MORPHISMS (Mathematics); MATHEMATICS; HYPERSPACE
- Publication
Commentarii Mathematici Helvetici, 2003, Vol 78, Issue 2, p335
- ISSN
0010-2571
- Publication type
Article
- DOI
10.1007/s000140300014