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Details of Grant 

EPSRC Reference: GR/N23271/01
Title: APPLICTIONS OF DERIVED CATEGORIES IN ALGEBRAIC GEOMETRY
Principal Investigator: Bridgeland, Professor T
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Sch of Mathematics
Organisation: University of Edinburgh
Scheme: Postdoc Res Fellowship PreFEC
Starts: 01 August 2001 Ends: 31 July 2003 Value (£): 63,164
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:  
Summary on Grant Application Form
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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Organisation Website: http://www.ed.ac.uk