Asymptotic Hodge theory and quantum products
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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 Kähler 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.
References and comments added. To appear in "Advances in Algebraic Geometry Motivated by Physics", Ed. E. Previatto, Contemporary Mathematics
References and comments added. To appear in "Advances in Algebraic Geometry Motivated by Physics", Ed. E. Previatto, Contemporary Mathematics