  We prove an existence theorem for jet differentials on complete intersection
varieties that generalizes a theorem of S. Diverio. We also show that one can
readily deduce hyperbolicity for generic complete intersections of high
multidegree from earlier work of Diverio-Merker-Rousseau and Diverio-Trapani.
And finally we prove the numerical aspect of a conjecture of O. Debarre.
