Positivity lemma

In this section we give a proof of Positivity Lemma (Lemma 3.3 of Bayer-Macrì's paper). The statement involves a divisor that is introduced in Definition 3.2. Briefly mention the relationship between their construction and the classical notion of determinant divisor (Proposition 4.4).

The result of the lemma is the nefness of this divisor, moreover the statement gives sufficient and necessary conditions for effectivity. The proof need some lemmas that are included in Section 3 of Bayer-Macrì's paper.