Diverio-Trapani conjecture on ampleness of invariant jet bundles

Let $Z\subset \mathbb{P}^n$ be the complete intersection of $c$-general hypersurfaces of sufficiently high degree. Let $E_{k,m}T_Z^*$ denote the invariant jet bundle of order $k$ and weighted degree $m$. Diverio-Trapani conjecture. The bundle $E_{k,m}T_Z^*$ is ample provided that

$$k\geqslant \frac{n}{c}-1$$

and $m\gg 0$. Motivated by Diverio's vanishing theorem for Green-Griffiths jet bundles, this conjecture generalizes Debarre's conjecture to higher-order invariant jet differentials. Its resolution is not indicated in the supplied text.