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We generalizes the main result of Demailly {D2} for the bundles Ek,mGG(V^*) of jet differentials of order k and weighted degree m to the bundles Ek,m(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.
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Mohammad Reza Rahmati (2025) studied this question.
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