Compatibility conjecture for the birational Abel–Jacobi correspondence

For generic $V\subset\Lambda^2W^*$, let $X$ and $Y$ be the associated Calabi–Yau varieties, and let $F(Y)$ and $H(X)$ be the birational moduli spaces described in the source. Since $H(X)$ is a moduli space on a Calabi–Yau manifold of dimension $2n-4$, it carries a natural $(2n-4)$-form. Compatibility conjecture. The birational isomorphism between $F(Y)$ and $H(X)$ is compatible with their $(2n-4)$-forms. The preceding theorem establishes that $F(Y)$, $G(Y)$, and $H(X)$ are birational for generic $V$; the supplied text does not state whether this compatibility assertion has been proved.