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Crepant resolutions and Hilb^G(C^4) for certain abelian subgroups for SL(4,C)
Published 15 May 2019 in math.AG | (1905.06244v2)
Abstract: Let G be a finite subgroup of SL(n,C), then the quotient Cn/G has a Gorenstein canonical singularity. Bridgeland-King-Reid proved that the G-Hilbert scheme HilbG(C3) gives a crepant resolution of the quotient C3/G for any finite subgroup G of SL(3,C). However, in dimension 4, very few crepant resolutions are known. In this paper, we will show several examples of crepant resolutions in dimension 4 and show examples in which HilbG(C4) is blow-up of certain crepant resolutions for C4/G, or HilbG(C4) has singularity.
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