Stability and existence of surfaces in symplectic 4-manifolds with b+=1

We establish various stability results for symplectic surfaces in symplectic 4-manifolds with b(+) = 1. These results are then applied to prove the existence of representatives of Lagrangian ADE-configurations as well as to classify negative symplectic spheres in symplectic 4-manifolds with kappa = -infinity. This involves the explicit construction of spheres in rational manifolds via a new construction technique called the tilted transport.