On projectively embeddable complex-foliated structures (Q713094)

Kodaira's famaous embedding theorem says that compact complex manifolds with a positive line bundle are projective algebraic. The author extends this to smoothly foliated manifolds with complex analytic leaves. He proves that they can be differentiably and tangentially holomorphically embedded into projective space provided they carry a tangentially holomorphic and posive line bundle. The proof relies on a parameter dependent version of Hörmander's estimates for the Cauchy-Riemann equations and a sophisticated approximation procedure based on the above estimates.