Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry
Assuming the standard framework of mirror symmetry, a conjecture is formulated describing how the diffeomorphism group of a Calabi-Yau manifold Y should act by families of Fourier-Mukai transforms over the complex moduli space of the mirror X. The conjecture generalizes a proposal of Kontsevich rela...
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| Format: | Book section |
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2001
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| Summary: | Assuming the standard framework of mirror symmetry, a conjecture is formulated describing how the diffeomorphism group of a Calabi-Yau manifold Y should act by families of Fourier-Mukai transforms over the complex moduli space of the mirror X. The conjecture generalizes a proposal of Kontsevich relating monodromy transformations and self-equivalences, Supporting evidence is given in the case of elliptic curves, lattice-polarized K3 surfaces and Calabi-Yau threefolds. A relation to the global Torelli problem is discussed. |
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