Implication of homological mirror symmetry

Let $X_b$ be a fiber of a Calabi–Yau threefold family and let $\hat X_0$ be its mirror. Write $F_B^\bullet$ and $F_A^\bullet$ for the Hodge filtrations on the respective stalks, let $Q$ be the intersection pairing, and let $\chi$ be the relative Euler characteristic on $K_0(\hat X_0)$. The mirror map at a fixed point $b$ is an isomorphism of the corresponding integral structures and polarized Hodge data. Implication of homological mirror symmetry. One has

$$mir_b: \left(H^{3}(X_b,\mathbb Z),F_B^\bullet,Q\right) \xrightarrow{\simeq} (K_0(\hat X_{0}),F_A^\bullet,\chi).$$

This expresses the expected compatibility between the B-model variation of Hodge structure and the A-model data arising from homological mirror symmetry, including the integral structure and polarization.