A vanishing theorem for semipositive line bundles over non-Kähler manifolds
The main result is the following. Let M be a compact complex manifold and L be a Hermitian holomorphic line bundle on M. Suppose the curvature form of L being everywhere semipositive and being strictly positive outside a set of measure zero. Then \(H^ q(M,LK_ M)=0\) for \(q\geq 1\), where \(K_ M\) is the canonical line bundle of M. A characterization of Moišezon manifolds is given. Connections with the conjecture of Grauert-Riemenschneider and the eigenvalue conjecture are discussed, too.
scientific article; zbMATH DE number 3923125