Let us consider the topological string A- and B-model (twisted SUSY non-linear sigma model on CY 3-manifold $X$). They are realization of $N=2$ SCFT and there are ground-states vector bundle $\mathcal{H}$ and vacuum line bundle $\mathcal{L}$ over the moduli space of the theory. In the A-model, $\mathcal{H}=H^{even}(X,\mathbb{C})$ and $\mathcal{L}=H^0(X,\mathbb{C})$. In the B-model, $\mathcal{H}=H^{3}(X,\mathbb{C})$ and $\mathcal{L}=H^{3,0}(X,\mathbb{C})$. The genus $g$ string amplitude is given as a section of $\mathcal{L}$ in either theory. Mirror symmetry is an identification of the geometry of A- and B-model ground-state geometry on distinct CY 3manifolds.
My questions is following. In the A-model, it seems the splitting of the bundle $$ \mathcal{H}_A=H^{even}(X,\mathbb{C})=\oplus_{i=0}^3 H^{2i}(X,\mathbb{C}) $$ does not vary over the moduli space of the theory (Kahler moduli space). On the other hand, in the B-model, the splitting $$ \mathcal{H}=H^{3}(X,\mathbb{C})=\oplus_{p+q=3}H^{p,q}(X,\mathbb{C}) $$ varies over the moduli space (variation of Hodge structure). Moreover, $\mathcal{L}$ is the trivial line bundle in the A-model, while it is not in the B-model. Isn't this contradiction?