Invariant Jet Differentials and Asymptotic Serre Duality

We generalizes the main result of Demailly D2 for the bundles E₊, ₌^GG (V^*) of jet differentials of order k and weighted degree m to the bundles E₊, ₌ (V^*) of the invariant jet differentials of order k and weighted degree m. We formulate and prove the existence of an asymptotic duality along the fibers of the Green-Griffiths jet bundles over projective manifolds.