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 |
[2] | DOI: 10.4310/ATMP.1999.v3.n3.a3 · Zbl 0976.32012 · doi:10.4310/ATMP.1999.v3.n3.a3 |
[3] | DOI: 10.1090/surv/068 · doi:10.1090/surv/068 |
[4] | DOI: 10.4310/ATMP.2002.v6.n4.a2 · doi:10.4310/ATMP.2002.v6.n4.a2 |
[5] | DOI: 10.4310/ATMP.1999.v3.n5.a5 · Zbl 0972.81135 · doi:10.4310/ATMP.1999.v3.n5.a5 |
[6] | DOI: 10.1016/S0550-3213(97)00282-4 · Zbl 0935.81058 · doi:10.1016/S0550-3213(97)00282-4 |
[7] | DOI: 10.1016/0550-3213(93)90033-L · Zbl 0910.14020 · doi:10.1016/0550-3213(93)90033-L |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.