Even and odd instanton bundles on Fano threefolds

We define non-ordinary instanton bundles on Fano threefolds $X$ extending the notion of (ordinary) bundles. determine a lower bound for quantum number bundle, i.e. degree its second Chern class, showing existence such each admissible value when $i_X\ge 2$ or $i_X=1$ and $\mathrm{Pic}(X)$ is cyclic. In these cases we deal with component inside moduli spaces simple containing vector construct study their restriction to lines. Finally give monadic description $\mathbb{P}^3$ smooth quadric studying loci jumping lines, expected codimension.