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Asymptotic Hodge theory and quantum products
Mathematics and Statistics Department Faculty Publication Series
Publication Date
2000
Abstract
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.
Citation Information
E Cattani and Javier Fernandez. "Asymptotic Hodge theory and quantum products" (2000) Available at: http://works.bepress.com/eduardo_cattani/22/
This is the pre-published version harvested from ArXiv.