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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].

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