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Picard-Fuchs equations and mirror maps for hypersurfaces

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arxiv hep-th/9111025 v1 pith:C32SAM5E submitted 1991-11-12 hep-th math.AG

Picard-Fuchs equations and mirror maps for hypersurfaces

David R. Morrison This is my paper
classification hep-th math.AG
keywords hypersurfacespicard-fuchscandelasequationsmirrorpredictionsquinticstrategy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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