Many people go through life without asking themselves the question: “When is a compact complex manifold an algebraic variety?” but not Japanese mathematician Kunihiko Kodaira. He made these kinds of questions his life’s work and got a Fields medal for his success. The Kodaira Embedding Theorem precisely characterizes which compact complex manifolds can be embedded in projective space. In this talk, we’ll go through some of the ideas involved in the theorem, its proof, and its applications.
