Let $\overline{M}_{0,0}(X, \beta)$ denote the moduli space of genus zero stable maps into $X$ that represent the homology class $\beta \in H_2(M, \mathbb{Z}) $. What does it mean to say that $~f:\mathbb{P}^1 \longrightarrow X $ is a ``free morphsim''? Secondly, what does it mean to say that $f$ is a free morphism that is birational onto its image?
Here $X$ is a compact complex surface.