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Title: Dihedral groups and G-Hilbert schemes
Author: Nolla de Celis, Álvaro
ISNI:       0000 0004 2673 3069
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2008
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics