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Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry

Abstract:
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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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Volume:
36
Pages:
317-337
Publication date:
2001
URN:
uuid:cc599e78-e811-43a9-83c0-e143f11f63ca
Source identifiers:
17218
Local pid:
pubs:17218

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