Crepant resolutions and Hilb^G(C^4) for certain abelian subgroups for SL(4,C)
Algebraic Geometry
2019-06-04 v2
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.
Keywords
Cite
@article{arxiv.1905.06244,
title = {Crepant resolutions and Hilb^G(C^4) for certain abelian subgroups for SL(4,C)},
author = {Y. Sato},
journal= {arXiv preprint arXiv:1905.06244},
year = {2019}
}
Comments
15 pages, 18 figures