2020/12/14 by Mohammad Reza Rahmati, Rahmati, Mohammad Reza
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2012.09024
We generalize the main result of Demailly \citeD2 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. Namely, Theorem 0.5 from \citeD2 and Theorem 9.3 from \citeD1 provide a lower bound (ck)/(k)mn+kr-1 on the number of the linearly independent holomorphic global sections of Ek,mGG V^* \bigotimes O(-m δA) for some ample divisor A. The group Gk of local reparametrizations of (ℂ,0) acts on the k-jets by orbits of dimension k, so that there is an automatic lower bound (ck)/(k) mn+kr-1 on the number of the linearly independent holomorphic global sections of Ek,mV^* \bigotimes O(-m δA). We formulate and prove the existence of an asymptotic duality along the fibers of the Green-Griffiths jet bundles over projective manifolds. We also prove a Serre duality for asymptotic sections of jet bundles. An application is also given for partial application to the Green-Griffiths conjecture.