LG/CY correspondence: The state space isomorphism |
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| Authors: | Alessandro Chiodo Yongbin Ruan |
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| Institution: | aInstitut Fourier, UMR du CNRS 5582, Université de Grenoble 1, BP 74, 38402, Saint Martin d?Hères, France;bDepartment of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA;cYangtze Center of Mathematics, Sichuan University, Chengdu 610064, PR China |
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| Abstract: | We prove the mirror duality conjecture for the mirror pairs constructed by Berglund, Hübsch, and Krawitz. Our main tool is a cohomological LG/CY correspondence which provides a degree-preserving isomorphism between the cohomology of finite quotients of Calabi–Yau hypersurfaces inside a weighted projective space and the Fan–Jarvis–Ruan–Witten state space of the associated Landau–Ginzburg singularity theory. |
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| Keywords: | MSC: 14J32 14J33 53C15 |
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