Cattani, EFernandez, Javier2024-04-262024-04-262000-01https://hdl.handle.net/20.500.14394/34209<p>This is the pre-published version harvested from ArXiv.</p>Assuming suitable convergence properties for the Gromov-Witten potential of a Calabi-Yau manifold $X$ one may construct a polarized variation of Hodge structure over the complexified K\"ahler cone of $X$. In this paper we show that, in the case of fourfolds, there is a correspondence between ``quantum potentials'' and polarized variations of Hodge structures that degenerate to a maximally unipotent boundary point. Under this correspondence, the WDVV equations are seen to be equivalent to the Griffiths' trasversality property of a variation of Hodge structure.article