“…The guideline is provided by an important theorem due to J.-P. Demailly [14] establishing the equivalence between the pseudo-effectivity of a line bundle and the existence of a closed positive current in its first Chern class (as recalled in 2.1). The notion of positively curved singular Hermitian vector bundle (and more generally, of a torsion-free coherent sheaf), as it has emerged from the articles [3], [38], [39] and [36], is recalled in sections 2.3 and 2.4 respectively. Next, the vector bundle counterpart of the pseudo-effectiveness is the notion of weak positivity, introduced by E. Viehweg, cf.…”