Crepant resolutions and Hilb^G(C⁴) for certain abelian subgroups for SL(4,C)

2019/05/15 by Sato, Y.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.06244

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 Hilb^G(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 Hilb^G(C⁴) is blow-up of certain crepant resolutions for C⁴/G, or Hilb^G(C⁴) has singularity.

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