An algorithm builds Calabi-Yau orientifolds and F-theory fourfold uplifts from 6d reflexive polytopes derived from orientifold data, with code in CYTools and GitHub.
Picard-Fuchs equations and mirror maps for hypersurfaces
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abstract
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.
fields
hep-th 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Generalizations beyond algebraic geometry in string theory remain aligned with mirror symmetry, support quantitative analysis, and point to deeper symplectic geometry connections.
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Calabi-Yau Orientifold Hypersurfaces and their F-theory Uplifts
An algorithm builds Calabi-Yau orientifolds and F-theory fourfold uplifts from 6d reflexive polytopes derived from orientifold data, with code in CYTools and GitHub.
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Beyond Algebraic Solutions to Stringy Spacetime
Generalizations beyond algebraic geometry in string theory remain aligned with mirror symmetry, support quantitative analysis, and point to deeper symplectic geometry connections.