| EPSRC Reference: |
GR/N23271/01 |
| Title: |
APPLICTIONS OF DERIVED CATEGORIES IN ALGEBRAIC GEOMETRY |
| Principal Investigator: |
Bridgeland, Professor T |
| Other Investigators: |
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| Department: |
Sch of Mathematics |
| Organisation: |
University of Edinburgh |
| Scheme: |
Postdoc Res Fellowship PreFEC |
| Starts: |
01 August 2001 |
Ends: |
31 July 2003 |
Value (£): |
63,164
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The language of derived categories seems to have an important role to play in the mathematical description of string theory. In particular, it has been conjectured that the numerical coincidences predicted by mirror symmetry are a consequence of an equivalence of derived categories. The aim of the project is to study in detail the properties of derived categories of sheaves on complex varieties and to give applications to certain well-known mathematical problems relating to string theory. To be more precise, applications are expected to the birational geometry of Calabi-Yau varieties and the higher-dimensional McKay correspondence. A related area of research will be the geometry of moduli spaces of vector bundles on higher-dimensional varieties. The idea here is to use the theory of Fourier-Mukai transforms (equivalencies of derived categories of sheaves) which have proved to be very successful tools for studying moduli spaces on surfaces.
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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 |