Kodaira 1953-1954 (Fields 1954): vanishing H^q(X, K_X otimes L)=0 for L positive q>=1; embedding theorem: X compact-Kahler + Hodge -> projective.
Kodaira 1953-1954 (Fields 1954): vanishing H^q(X, K_X otimes L)=0 for L positive q>=1; embedding theorem: X compact-Kahler + Hodge -> projective.