| EPSRC Reference: |
GR/S03980/01 |
| Title: |
Algebraic geometry, graded rings and computer algebra |
| Principal Investigator: |
Reid, Professor M |
| Other Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
University of Warwick |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 April 2003 |
Ends: |
30 September 2005 |
Value (£): |
146,277
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Logic & Combinatorics |
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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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The study of 3-folds by Kawamata, Koll'ar, Mori, Mukai, Reid and others over the last 20 years leads to a vast number of new problems with a computational flavour. Reid and several of his students have used computers in an ad hoc way in compiling lists of (singular) K3 surfaces and Fano 3folds, and more recently, Brown has written a first working version of a database of K3 surfaces, included in export 2.8 of Magma. The proposed project will complete the work on this database, and generalise it to cover Calabi-Yau 3-folds, Fano 3-folds and 4-folds, etc. The complete classification of (singular) Fano 3-folds and birational links between them is a major algebraic geometric ambition, and computer algebra has a central role to play in this. While database techniques handle the combinatorics of long lists of varieties and birational links between them, the existence, moduli, fields of definition, etc., of these varieties provide a natural meeting ground of algebraic geometry and computer algebra. The project will teach UK and European mathematicians to use computer algebra in attacking algebraic geometry problems; it will also provide a huge range of problems to test and add to the capabilities of Magma.
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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.warwick.ac.uk |