{$\sum a_i[C_i] \vert C_i$ is a $J$-holomorphic curve, $a_i \in {{\mathbb}{R}}~\text{and } a_i\geq 0 $.}

Define the symplectic effective cone $SNE(V) = \cap NEJ(V)$ for all compatible $J$.

Define the deformed symplectic effective cone $DNE(V) = \cap SNE(V)$ for all the symplectic forms which can be deformed to $\omega$.

Since Gromov-Witten invariants are symplectic deformation invariant and are zero if the moduli space of $J$-holomorphic curves is empty for some almost complex structure $J$, we get the following corollary.

\[cor:extremal\] Extremal rays listed in Theorem \[thm:extremal\] on smooth projective $4$-folds are symplectic and deformed symplectic extremal.

This corollary, in particular, shows that all such extremal rays lie in the *effective* cone of any variety symplectic deformation equivalent to the given variety. Note that this is the best one can hope for since the surface ${{\mathbb}{P}}^1 \times {{\mathbb}{P}}^1$ will deform to the Hirzebruch surface ${{\mathbb}{F}}_2$ and only one of the two extremal rays stay extremal (but both stay effective). We expect that all the extremal rays stay effective under symplectic deformations. Such a statement will follow if one can show all the extremal rays support some curve class which gives a non-zero Gromov-Witten invariant. It seems that there is no way 