Asymptotic Hodge theory and quantum products
This is the pre-published version harvested from ArXiv.http://arxiv.org/abs/math/0011137
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.
E Cattani and Javier Fernandez. "Asymptotic Hodge theory and quantum products" 2000
Available at: http://works.bepress.com/eduardo_cattani/22