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Asymptotic Hodge theory and quantum products

Eduardo Cattani·Javier Fernandez
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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 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.

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Eduardo Cattani, Javier Fernandez. 2000-11-26. Asymptotic Hodge theory and quantum products. https://arxiv.org/abs/math/0011137

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