Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence

Chiodo, Alessandro; Iritani, Hiroshi; Ruan, Yongbin

Publications Mathématiques de l'IHÉS, Tome 119 (2014), pp. 127-216.

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 $\widehat{\Gamma }$-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.

Mots clés : Integral Structure, Chern Character, Quantum Cohomology, Twisted Theory, Frobenius Manifold

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