An analytical proof of Kodaira's embedding theorem for Hodge manifolds (Q1058023)

The purpose of this paper is to provide a differential geometric proof for the well-known Kodaira embedding theorem for Hodge manifolds \(\tilde M\) with \(\dim \tilde M\geq 2.\) Since \(\tilde M\) is Hodge, so it carries a negative line bundle F. Let M' be the holomorphic \({\mathbb{C}}^*\)-bundle associated to F and let \(\pi ': M'\to \tilde M\) be the projection. Now let M be the U(1) reduction of M'. In view of the negativity of F, M is actually a compact strongly pseudoconvex real hypersurface of M'. Inspired by some technique of Boutet de Monvel who observed that M can be embedded in some affine space \({\mathbb{C}}^ N\), the author shows that, by using some estimation technique due to Kohn, such an embedding induces an embedding of M into some \({\mathbb{P}}_{N-1}\).