A note on asymptotic Serre duality for jet differentials
  We formulate and prove the existence of an asymptotic duality along the fibers of the Green-Griffiths jet bundles over projective manifolds. The existence of global sections for these bundles and also for their dual sheaves has been established by the author and J. P. Demailly in a previous article, [3]. 
Mohammad Reza Rahmati
math.AG