EPSRC Reference: 
GR/N23271/01 
Title: 
APPLICTIONS OF DERIVED CATEGORIES IN ALGEBRAIC GEOMETRY 
Principal Investigator: 
Bridgeland, Professor T 
Other Investigators: 

Researcher CoInvestigators: 

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: 

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 wellknown mathematical problems relating to string theory. To be more precise, applications are expected to the birational geometry of CalabiYau varieties and the higherdimensional McKay correspondence. A related area of research will be the geometry of moduli spaces of vector bundles on higherdimensional varieties. The idea here is to use the theory of FourierMukai transforms (equivalencies of derived categories of sheaves) which have proved to be very successful tools for studying moduli spaces on surfaces.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.ed.ac.uk 