Fourier-Mukai transforms for K3 and elliptic fibrations
Given a non-singular variety with a K3 fibration π: X → S we construct dual fibrations π̂ : Y → S by replacing each fibre Xs of π by a two-dimensional moduli space of stable sheaves on Xs. In certain cases we prove that the resulting scheme Y is a non-singular variety and construct an equivalence of...
| Principais autores: | , |
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| Formato: | Journal article |
| Idioma: | English |
| Publicado em: |
2002
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| _version_ | 1826264892511879168 |
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| author | Bridgeland, T Maciocia, A |
| author_facet | Bridgeland, T Maciocia, A |
| author_sort | Bridgeland, T |
| collection | OXFORD |
| description | Given a non-singular variety with a K3 fibration π: X → S we construct dual fibrations π̂ : Y → S by replacing each fibre Xs of π by a two-dimensional moduli space of stable sheaves on Xs. In certain cases we prove that the resulting scheme Y is a non-singular variety and construct an equivalence of derived categories of coherent sheaves Φ: D(Y) → D (X). Our methods also apply to elliptic and abelian surface fibrations. As an application we use the equivalences Φ to relate moduli spaces of stable bundles on elliptic threefolds to Hilbert schemes of curves. |
| first_indexed | 2024-03-06T20:15:09Z |
| format | Journal article |
| id | oxford-uuid:2be64081-0b05-498f-9d3e-07af16f2ef66 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:15:09Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:2be64081-0b05-498f-9d3e-07af16f2ef662022-03-26T12:33:41ZFourier-Mukai transforms for K3 and elliptic fibrationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2be64081-0b05-498f-9d3e-07af16f2ef66EnglishSymplectic Elements at Oxford2002Bridgeland, TMaciocia, AGiven a non-singular variety with a K3 fibration π: X → S we construct dual fibrations π̂ : Y → S by replacing each fibre Xs of π by a two-dimensional moduli space of stable sheaves on Xs. In certain cases we prove that the resulting scheme Y is a non-singular variety and construct an equivalence of derived categories of coherent sheaves Φ: D(Y) → D (X). Our methods also apply to elliptic and abelian surface fibrations. As an application we use the equivalences Φ to relate moduli spaces of stable bundles on elliptic threefolds to Hilbert schemes of curves. |
| spellingShingle | Bridgeland, T Maciocia, A Fourier-Mukai transforms for K3 and elliptic fibrations |
| title | Fourier-Mukai transforms for K3 and elliptic fibrations |
| title_full | Fourier-Mukai transforms for K3 and elliptic fibrations |
| title_fullStr | Fourier-Mukai transforms for K3 and elliptic fibrations |
| title_full_unstemmed | Fourier-Mukai transforms for K3 and elliptic fibrations |
| title_short | Fourier-Mukai transforms for K3 and elliptic fibrations |
| title_sort | fourier mukai transforms for k3 and elliptic fibrations |
| work_keys_str_mv | AT bridgelandt fouriermukaitransformsfork3andellipticfibrations AT maciociaa fouriermukaitransformsfork3andellipticfibrations |