# How do one show that the quotient space is a projective manifold?

I want to prove the following statement.

Let $$\Omega$$ be a bounded domain, and $$\Gamma \subset \text{Aut}(\Omega)$$ be the subgroup acting totally discontinuously on $$\Omega$$ without fixed points such that the quotient space $$X = \Omega \setminus \Gamma$$ is a compact complex manifold. Then $$X$$ is a projective manifold.

My idea is to use the Kodaira Emdedding theorem by constructing a positive holomorphic line bundle. However, I am not sure how to do so. Can you provide me with some ideas how to do so? Thank you.

In brief, the canonical bundle of the quotient manifold is positive (one uses a curvature computation for the Bergman metric on $$K_\Omega$$), hence, Kodaira's embedding theorem applies.