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Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry

Balazs Szendroi
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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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BibTeXRIS

Balazs Szendroi. 2001-03-26. Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry. https://arxiv.org/abs/math/0103137

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