| EPSRC Reference: |
GR/S42460/01 |
| Title: |
Cohomology of Quotients: Moduli Spaces of Hypersurfaces in Toric Varieties |
| Principal Investigator: |
Kirwan, Professor FC |
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| Department: |
Mathematical Institute |
| Organisation: |
University of Oxford |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
14 December 2003 |
Ends: |
13 December 2005 |
Value (£): |
86,731
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The study of moduli spaces is of fundamental importance to modern geometry, and is increasingly important to mathematical physics as well. Moduli spaces arise in classification problems in geometry, when, as is typically the case, there are not enough discrete invariants to classify objects completely. The points in a moduli space correspond bijectively with isomorphism classes of the objects to be classified, and its geometric structure reflects the way the objects can vary in families depending on parameters. Understanding the topology of moduli spaces is crucial to many geometrical problems.This project aims to study the topology of certain classes of moduli spaces which have relevance to both mathematicians and physicists, including moduli spaces of hypersurfaces (and more generally complete intersections) in toric varieties. These moduli spaces can be constructed as quotient spaces for group actions, where the groups involved (typically automorphism groups of toric varieties) are not reductive. This means that well known methods for studying the topology of quotients by reductive groups will need to be extended to the non-reductive case.
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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 |
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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.ox.ac.uk |