Picard-Fuchs equations and mirror maps for hypersurfaces. (English) Zbl 0841.32013

Yau, Shing-Tung (ed.), Essays on mirror manifolds. Cambridge, MA: International Press. 241-264 (1992).
The author considers the Picard-Fuchs equation \({d^s f \over dz^s} + \sum^{s - 1}_{j = 0} C_j (z) {d^j f \over dz^j} = 0\), to compute Yukawa couplings and the mirror map. Using a technique due to Griffiths, he is able to compute Picard-Fuchs equations of hypersurfaces.
Explicit examples are shown for certain one-parameter families of Calabi-Yau threefolds.
As an application, the author predicts the number of rational curves on the weighted projective hypersurfaces.
For the entire collection see [Zbl 0816.00010].


32G20 Period matrices, variation of Hodge structure; degenerations
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
14J10 Families, moduli, classification: algebraic theory
Full Text: arXiv