Dihedral groups and G-Hilbert schemes
Nolla de Celis, Álvaro (2008) Dihedral groups and G-Hilbert schemes. PhD thesis, University of Warwick.
WRAP_THESIS_NollaDeCelis_2008.pdf - Draft Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://webcat.warwick.ac.uk/record=b2280120~S15
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|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute|
|Supervisor(s)/Advisor:||Reid, Miles (Miles A.)|
|Format of File:|
|Extent:||112 leaves : charts|
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