Positivity of Ulrich bundles in the ample and free case

In this paper, we study the positivity of an Ulrich vector bundle defined with respect to a globally generated ample line bundle. First, we prove a generalization of a Lopez theorem on the first Chern class and the bigness of an Ulrich bundle. Then, under some additional assumptions on the polarization, we give a description of its augmented base locus, which consequently leads to a characterization of the V-bigness and of the ampleness of an Ulrich bundle in this setting.