| EPSRC Reference: |
GR/M36601/01 |
| Title: |
EXTENDING FOURIER-MUKAI DUALITIES TO HIGHER DIMENSIONAL FIBRATIONS |
| Principal Investigator: |
Maciocia, Professor A |
| Other Investigators: |
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| Department: |
Sch of Mathematics |
| Organisation: |
University of Edinburgh |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
11 November 1998 |
Ends: |
10 November 2000 |
Value (£): |
72,020
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Physics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Fourier-Mukai transforms are a powerful tool in the study of sheaves and bundles on varieties, especially those relevant in physics. Such transforms have been classified by Maciocia and Bridgeland for the case of dimension 2 varieties and this project aims to extend part of this classification to the case of surface and curve fibred varieties in higher dimensions. This is an extension of the successful technique used to complete the classification for surfaces via elliptic surfaces. The methods used will be deformation theoretic to compute moduli spaces or sheaves on fibrations with singular or non-reduced fibres as well as powerful techniques from derived category theory. We shall proceed by first completing the work Tom has done in his thesis on FM transforms for elliptically fibred varieties. We shall then use similar methods to construct FM transforms on surface fibred varieties. The FM transforms will be applied to compute the birational geometry of moduli spaces of stable sheaves and bundles on such varieties.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ed.ac.uk |