In McDuff-Salamon’s book “J holomorphic curves and Symplectic topology” they define the space $M^*_{0,k}(A,J)$ to be the moduli space of simple $J$-holomorphic curves of genus 0 with $k$ marked points in the homology class $A$.

My question is how does one interpret the definition of the moduli space $M^*_{0,k}(0,J)$.

1)I understand that as the homology class is 0, these are all constant maps but what does being a simple map mean in this context?

- They also mention that $M^*_{0,k}(0,J)$ is empty for $k < 3$. I presume this has something to do with the 3-transitivity of the $PSL(2,mathbb{C})$ action on $S^2$ but could someone explain why this is the case?