2000/11/26 by Eduardo Cattani, Javier Fernandez
Mathematics · #math.AG #msc:14D07 #msc:14N35 #msc:32G20 #msc:14J32
published as Contemporary Mathematics, 276 (2001), p. 115-136. · References and comments added. To appear in "Advances in Algebraic Geometry Motivated by Physics", Ed. E. Previatto, Contemporary Mathematics
arxiv created 2000/11/26 · arxiv updated 2009/11/30
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.