Asymptotic Hodge theory and quantum products
Algebraic Geometry
2007-05-23 v2
Abstract
Assuming suitable convergence properties for the Gromov-Witten potential of a Calabi-Yau manifold one may construct a polarized variation of Hodge structure over the complexified K\"ahler cone of . 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.
Cite
@article{arxiv.math/0011137,
title = {Asymptotic Hodge theory and quantum products},
author = {Eduardo Cattani and Javier Fernandez},
journal= {arXiv preprint arXiv:math/0011137},
year = {2007}
}
Comments
References and comments added. To appear in "Advances in Algebraic Geometry Motivated by Physics", Ed. E. Previatto, Contemporary Mathematics