  The paper studies a relation between fundamental group of the complement to a
plane singular curve and the orbifold pencils containing it. The main tool is
the use of Albanese varieties of cyclic covers ramified along such curves. Our
results give sufficient conditions for a plane singular curve to belong to an
orbifold pencil, i.e. a pencil of plane curves with multiple fibers inducing a
map onto an orbifold curve whose orbifold fundamental group is non trivial. We
construct an example of a cyclic cover of the projective plane which is an
abelian surface isomorphic to the Jacobian of a curve of genus 2 illustrating
the extent to which these conditions are necessary.
