The application of Seiberg-Witten theory to the study of smooth 4-manifolds over the last three years has proved extremely fruitful. In particular, progress has been made concerning the '11/8s' conjecture and the minimal genus problem. In this dissertation, we extend a '10/8s' result of Furuta to a special group of spin 4-orbifolds. This result yields information concerning the minimal genus problem of representing homology classes of a smooth 4-manifold by embedded surfaces
