If $G$ is a complex semi simple Lie group and $P$ is a parabolic subgroup of it, the quotient $G/P$ is endowed with a Kahler structure and the action of $G$ on $G/P$ is holomorphic with respect to this structure. For $A\in H_2(G/P, \mathbb{Z})$ we define $\mathcal{M}_A$ as the moduli space of homolomorphic curves $\mu:\mathbb{CP}^1\to G/P$ whose degree is $A.$