Published online by Cambridge University Press: 20 November 2018
Let $f:\,E\,\to \,B$ 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
${{\text{ }\!\!\pi\!\!\text{ }}_{1}}\left( {{F}_{b}} \right)\,\to \,{{\text{ }\!\!\pi\!\!\text{ }}_{1}}\,\left( E \right)$ induced by the inclusion is injective.