Asymptotic Hodge theory and quantum products

Details Asymptotic Hodge theory and quantum products Asymptotic Hodge theory and quantum products

2000-11-19

arxiv.org/abs/math/0011137v2

Contemporary Mathematics, 276 (2001), p. 115-136.

Mathematics

Algebraic Geometry

References and comments added. To appear in "Advances in Algebraic Geometry Motivated by Physics", Ed. E. Previatto, Contempor

Scientific paper

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.

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