Crepant resolutions and Hilb^G(C^4) for certain abelian subgroups for SL(4,C)
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2019
- DOI:
- 10.48550/arXiv.1905.06244
- arXiv:
- arXiv:1905.06244
- Bibcode:
- 2019arXiv190506244S
- Keywords:
-
- Mathematics - Algebraic Geometry
- E-Print:
- 15 pages, 18 figures