# sg.symplectic geometry – Moduli space of constant maps

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?

1. 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?