Crepant resolutions and A-Hilbert schemes in dimension four
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
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)|
|Subjects:||Q Science > QA Mathematics|
|Library of Congress Subject Headings (LCSH):||Singularities (Mathematics), Hilbert schemes|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute|
|Supervisor(s)/Advisor:||Reid, Miles (Miles A.)|
|Sponsors:||Korea (R33-2008-000-10101-0) ; Nagoya Daigaku|
|Extent:||126 leaves : ill.|
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