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Crepant resolutions and A-Hilbert schemes in dimension four
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Davis, Sarah Elizabeth (2012) Crepant resolutions and A-Hilbert schemes in dimension four. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2584703~S1
Abstract
The aim of this thesis is to improve our understanding of when crepant resolutions exist in dimension four. In three dimensions [BKR01] proved that for any finite subgroup G ⊂ SL(3,C) the G-Hilbert scheme G-Hilb(C3) gives a crepant resolution of the quotient singularity C3/G. In four dimensions very little is known about when crepant resolutions exist. In this thesis I present several approaches to this problem. I give an algorithm which determines, for quotients by cyclic subgroups of SL(4,C) whether or not a crepant resolution exists. This algorithm seeks to find a crepant resolution by performing a tree search. In Chapter 4, building on the work of [CR02] in three dimensions, I calculate the A-Hilbert scheme for a family of abelian subgroups A ⊂ SL(4,C). I show that this can be used to find a crepant resolution of C4/A.
| Item Type: | Thesis or Dissertation (PhD) |
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| Subjects: | Q Science > QA Mathematics |
| Library of Congress Subject Headings (LCSH): | Singularities (Mathematics), Hilbert schemes |
| Date: | March 2012 |
| Institution: | University of Warwick |
| Theses Department: | Mathematics Institute |
| Thesis Type: | PhD |
| Publication Status: | Unpublished |
| Supervisor(s)/Advisor: | Reid, Miles (Miles A.) |
| Sponsors: | Korea (R33-2008-000-10101-0) ; Nagoya Daigaku |
| Extent: | 126 leaves : ill. |
| Language: | eng |
| URI: | http://wrap.warwick.ac.uk/id/eprint/49105 |
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