Let $X$ be a sympletic manifold and $A\in H_2(X;\mathbb{Q})$. Let $g$ and $k$ be nonnegative integers. Assume that $$\mathcal{M}_{g,k}(X;A)$$

is dense in

$$\overline{\mathcal{M}}_{g,k}(X;A).$$

Are the primary Gromov-Witten invariants corresponding to $X$ and $A$ enumerative?

If not, when does the condition $$\mathcal{M}_{g,k}(X;A)$$

dense in

$$\overline{\mathcal{M}}_{g,k}(X;A)$$

imply that the corresponding primary Gromov-Witten invariants are enumerative?