An integral structure in quantum cohomology and mirror symmetry for toric orbifolds |
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Authors: | Hiroshi Iritani |
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Institution: | a Faculty of Mathematics, Kyushu University, 6-10-1, Hakozaki, Higashiku, Fukuoka 812-8581, Japan b Department of Mathematics, Imperial College London, Huxley Building, 180, Queen's Gate, London SW7 2AZ, United Kingdom |
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Abstract: | We introduce an integral structure in orbifold quantum cohomology associated to the K-group and the -class. In the case of compact toric orbifolds, we show that this integral structure matches with the natural integral structure for the Landau-Ginzburg model under mirror symmetry. By assuming the existence of an integral structure, we give a natural explanation for the specialization to a root of unity in Y. Ruan's crepant resolution conjecture Yongbin Ruan, The cohomology ring of crepant resolutions of orbifolds, in: Contemp. Math., vol. 403, Amer. Math. Soc., Providence, RI, 2006, pp. 117-126]. |
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Keywords: | Quantum cohomology Variation of Hodge structures Semi-infinite variation of Hodge structures Mirror symmetry Landau-Ginzburg model Toric Deligne-Mumford stack Orbifold Orbifold quantum cohomology Crepant resolution conjecture Ruan's conjecture K-theory McKay correspondence Oscillatory integral Hypergeometric function GKZ-system Singularity theory Gamma class |
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