A notion of $\Delta$-multigenus for certain rank two ample vector bundles

A notion of ``delta-genus" for ample vector bundles $\E$ of rank two on a smooth projective threefold $X$ is defined as a couple of integers $(\delta_1,\delta_2)$. This extends the classical definition holding for ample line bundles. Then pairs $(X,\E)$ with low $\delta_1$ and $\delta_2$ are classified under suitable additional assumptions on $\E$