.$$ Then we have the exact sequence $$0 \to \OO_Y(-F_Y) \to \bigwedge^r\mathcal E \to \mathcal Q \to 0.$$ Since $\OO_Y(-F_Y)$ is saturated in $\bigwedge^r\mathcal E$, the sheaf $\mathcal Q$ is torsion free, and hence $F=c_0(\mathcal Q)$ is pseudoeffective by Theorem \[thm:CP00\]. From the above exact sequence, there exists a positive integer $\ell$ such that $\ell K_Y\sim