Kähler cone (${\mathcal{K}}_M$)

The Kähler cone of a compact Kähler manifold is the open cone of real $(1,1)$ cohomology classes represented by positive closed $(1,1)$ forms. If every real degree-two cohomology class has type $(1,1)$, density of rational classes supplies a rational Kähler class. An integral multiple is the First Chern class of a positive holomorphic line bundle, and the Kodaira embedding theorem implies projectivity.