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Dihedral groups and G-Hilbert schemes
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Nolla de Celis, Álvaro (2008) Dihedral groups and G-Hilbert schemes. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2280120~S15
Abstract
Let G ⊂ GL(2,C) be a finite subgroup acting on the complex plane C2, and consider the following diagram
C2 -> X <- π:Y
where π is the minimal resolution of singularities. Since Du Val in the 1930s the explicit calculation of Y was made from X by blowing up the singularity at the origin, where we lose any information about the group G in the process. But, is there a direct relation between the resolution Y and the group G?
McKay [McK80] in the late 1970s was the first to realise the link between the group action and the resolution Y , thus giving birth to the so called McKay correspondence. This beautiful correspondence establishes an equivalence between the geometry of the minimal resolution Y of the quotient singularity C2/G, and the G-equivariant geometry of C2.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Symmetry groups, Symmetry (Mathematics), Hilbert schemes, Schemes (Algebraic geometry), Group theory | ||||
Official Date: | 2008 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Reid, Miles (Miles A.) | ||||
Format of File: | |||||
Extent: | 112 leaves : charts | ||||
Language: | eng |
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