In this talk, I will explain a new compactification of the moduli space of (pseudo)-holomorphic maps from a compact Riemann surface with prescribed singularity types. Main emphasis of the talk will lie on a key component of the compactification; a compactificaiton of the moduli space of rational maps in the projective space relative to the hyperplane at infinity and modulo homothety and translations. This is a joint work with Kenji Fukaya.