Nolla de Celis, Álvaro (2008) Dihedral groups and G-Hilbert schemes. PhD thesis, University of Warwick.

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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 or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Symmetry groups, Symmetry (Mathematics), Hilbert schemes, Schemes (Algebraic geometry), Group theory
Date:	September 2008
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Reid, Miles (Miles A.)
Format of File:	pdf
Extent:	112 leaves : charts
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/2000

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