On plane algebraic curves of positive Albanese dimension

A notion of Albanese dimension of a plane algebraic curve is introduced as the maximum of the dimensions of the images of Albanese mapping of cyclic coverings of the plane ramified along this curve. A necessary condition for a curve to have Albanese dimension equal to one is given in terms of its equation. This condition is sufficient for a generic curve. A complete description of the Alexander polynomials of plane curves of Albanese dimension one is given. Also the images of the Albanese mappings of cyclic coverings ramified along such curves are described completely.