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arXiv · 1905.06244

Crepant resolutions and Hilb^G(C^4) for certain abelian subgroups for SL(4,C)

Y. Sato
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Abstract

Let G be a finite subgroup of SL(n,C), then the quotient C^n/G has a Gorenstein canonical singularity. Bridgeland-King-Reid proved that the G-Hilbert scheme Hilb^G(C^3) gives a crepant resolution of the quotient C^3/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 Hilb^G(C^4) is blow-up of certain crepant resolutions for C^4/G, or Hilb^G(C^4) has singularity.

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Y. Sato. 2019-05-15. Crepant resolutions and Hilb^G(C^4) for certain abelian subgroups for SL(4,C). https://arxiv.org/abs/1905.06244

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