  It is a well known fact that every embedded symplectic surface $\Sigma$ in a
symplectic 4-manifold $(X^4,\omega)$ can be made $J$-holomorphic for some
almost-complex structure $J$ compatible with $\omega$. In this paper we
investigate when such a $J$ can be chosen from a generic set of almost-complex
structures. As an application we give examples of smooth and non-empty
Seiberg-Witten and Gromov-Witten moduli spaces whose associated invariants are
zero.
