The eventual paracanonical map of a variety of maximal Albanese dimension

Let X be a smooth complex projective variety such that the Albanese map of X is generically finite onto its image. Here, we study the so-called eventual m-paracanonical map of X, whose existence is implied by previous results of the authors (when m = 1, we also assume chi(K-X) > 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 by Beauville, while it is birational for m > 1. We also describe it explicitly in several examples.