On the connection between fundamental groups and pencils with multiple fibers

We present two results about the relationship between fundamental groups of quasiprojective manifolds and linear systems on a projectivization. We prove the existence of a plane curve with non-abelian fundamental group of the complement which does not admit a mapping onto an orbifold with non-abelian fundamental group. We also find an affine manifold whose irreducible components of its characteristic varieties do not come from the pull-back of the characteristic varieties of an orbifold.