Picard-Fuchs equations and mirror maps for hypersurfaces

Details Picard-Fuchs equations and mirror maps for hypersurfaces Picard-Fuchs equations and mirror maps for hypersurfaces

1991-11-12

arxiv.org/abs/hep-th/9111025v1

Physics

High Energy Physics

High Energy Physics - Theory

23 pages

Scientific paper

We describe a strategy for computing Yukawa couplings and the mirror map, based on the Picard-Fuchs equation. (Our strategy is a variant of the method used by Candelas, de la Ossa, Green, and Parkes in the case of quintic hypersurfaces.) We then explain a technique of Griffiths which can be used to compute the Picard-Fuchs equations of hypersurfaces. Finally, we carry out the computation for four specific examples (including quintic hypersurfaces, previously done by Candelas et al.). This yields predictions for the number of rational curves of various degrees on certain hypersurfaces in weighted projective spaces. Some of these predictions have been confirmed by classical techniques in algebraic geometry.

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