The eventual paracanonical map of a variety of maximal Albanese dimension

Let Xbe a smooth complex projective variety such that the Albanese map of Xis generically ?nite onto its image. Here we study the so-called eventual m-paracanonical map of X, whose existence is implied by the results of [4] (when m= 1 we also assume ?(KX)>0). We show that for m= 1 this map behaves in a similar way to the canonical map of a surface of general type, as described in [6], while it is birational for m > 1. We also describe it explicitly in several examples.