Extending the Picard-fuchs system of local mirror symmetry. (English) Zbl 1110.32011
Summary: We propose an extended set of differential operators for local mirror symmetry. If \(X\) is Calabi-Yau such that dim \(H_{4}(X,\mathbb Z)=0\), then we show that our operators fully describe mirror symmetry. In the process, a conjecture for intersection theory for such \(X\) is uncovered. We also find operators on several examples of type \(X=K_{S}\) through similar techniques. In addition, open string Picard-Fuchs systems are considered.
MSC:
| 32Q25 | Calabi-Yau theory (complex-analytic aspects) |
| 14D05 | Structure of families (Picard-Lefschetz, monodromy, etc.) |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 32G20 | Period matrices, variation of Hodge structure; degenerations |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
References:
| [1] | DOI: 10.1016/S0550-3213(01)00228-0 · Zbl 0983.81050 · doi:10.1016/S0550-3213(01)00228-0 |
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| [7] | DOI: 10.1016/0550-3213(93)90033-L · Zbl 0910.14020 · doi:10.1016/0550-3213(93)90033-L |
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