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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| _version_ | 1826297012218232832 |
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| author | Szendroi, B |
| author_facet | Szendroi, B |
| author_sort | Szendroi, B |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T04:25:07Z |
| format | Book section |
| id | oxford-uuid:cc599e78-e811-43a9-83c0-e143f11f63ca |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:25:07Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:cc599e78-e811-43a9-83c0-e143f11f63ca2022-03-27T07:21:24ZDiffeomorphisms and families of Fourier-Mukai transforms in mirror symmetryBook sectionhttp://purl.org/coar/resource_type/c_3248uuid:cc599e78-e811-43a9-83c0-e143f11f63caSymplectic Elements at Oxford2001Szendroi, BAssuming 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. |
| spellingShingle | Szendroi, B Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry |
| title | Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry |
| title_full | Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry |
| title_fullStr | Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry |
| title_full_unstemmed | Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry |
| title_short | Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry |
| title_sort | diffeomorphisms and families of fourier mukai transforms in mirror symmetry |
| work_keys_str_mv | AT szendroib diffeomorphismsandfamiliesoffouriermukaitransformsinmirrorsymmetry |