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On the Zariski-van Kampen Theorem

  Published:2003-02-01
 Printed: Feb 2003
  • Ichiro Shimada
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Abstract

Let $f \colon E\to B$ be a dominant morphism, where $E$ and $B$ are smooth irreducible complex quasi-projective varieties, and let $F_b$ be the general fiber of $f$. We present conditions under which the homomorphism $\pi_1 (F_b)\to \pi_1 (E)$ induced by the inclusion is injective.
MSC Classifications: 14F35 show english descriptions Homotopy theory; fundamental groups [See also 14H30] 14F35 - Homotopy theory; fundamental groups [See also 14H30]
 

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