Geodesic
Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence
Chiodo, Alessandro1  ; Iritani, Hiroshi2  ; Ruan, Yongbin3 
1 Institut de Mathématiques de Jussieu, UMR 7586 CNRS, Université Pierre et Marie Curie Case 247, 4 Place Jussieu 75252 Paris cedex 05 France
2 Department of Mathematics, Graduate School of Science, Kyoto University Kitashirakawa-Oiwake-cho, Sakyo-ku 606-8502 Kyoto Japan
3 Department of Mathematics, University of Michigan 48109-1109 Ann Arbor MI USA
Publications Mathématiques de l'IHÉS, Tome 119 (2014), pp. 127-216

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We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan, Jarvis and Ruan following a proposal of Witten. Moreover, on both sides, we highlight two remarkable integral local systems arising from the common formalism of Γ ^-integral structures applied to the derived category of the hypersurface {W=0} and to the category of graded matrix factorizations of W. In this setup, we prove that the analytic continuation matches Orlov equivalence between the two above categories.

DOI : 10.1007/s10240-013-0056-z
Keywords: Integral Structure, Chern Character, Quantum Cohomology, Twisted Theory, Frobenius Manifold

Chiodo, Alessandro 1 ; Iritani, Hiroshi 2 ; Ruan, Yongbin 3

1 Institut de Mathématiques de Jussieu, UMR 7586 CNRS, Université Pierre et Marie Curie Case 247, 4 Place Jussieu 75252 Paris cedex 05 France
2 Department of Mathematics, Graduate School of Science, Kyoto University Kitashirakawa-Oiwake-cho, Sakyo-ku 606-8502 Kyoto Japan
3 Department of Mathematics, University of Michigan 48109-1109 Ann Arbor MI USA 
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     author = {Chiodo, Alessandro and Iritani, Hiroshi and Ruan, Yongbin},
     title = {Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and {Orlov} equivalence},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {127--216},
     publisher = {Springer Berlin Heidelberg},
     address = {Berlin/Heidelberg},
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Chiodo, Alessandro; Iritani, Hiroshi; Ruan, Yongbin. Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence. Publications Mathématiques de l'IHÉS, Tome 119 (2014), pp. 127-216. doi: 10.1007/s10240-013-0056-z

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