There is no enough room here to write the answer to your question. However, you can take a look at the appendix of Hartshorne and if you have time, a classical reference is Griffiths and Harris: Principles in algebraic geometry. However roughly speaking, the concept of positivity will tell you that a compact Kahler complex manifold is algebraic.

There is no enough room here to write the answer to your question. However, you can take a look at the appendix of Hartshorne and if you have time, a classical reference is Griffiths and Harris: Principles in algebraic geometry. However roughly speaking, the concept of positivity will tell you when a compact Kahler complex manifold is algebraic.