Moduli spaces $M_{g,n}(W)$ for surfaces
  We construct and prove the projectiveness of the moduli spaces which are natural generalizations to the case of surfaces of the following:   1) $M_{g,n}$, the moduli space of $n$-marked stable curves,   2) $M_{g,n}(W)$, the moduli space of $n$-marked stable maps to a variety $W$. 
Valery Alexeev