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

Albanese varieties of cyclic covers of the projective plane and orbifold pencils