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Crepant partial resolutions of the nilpotent cone via Hamiltonian reduction
Abstract
We show that the nilpotent cone associated to a simply connected semisimple algebraic group, together with all its crepant projective partial resolutions, can be constructed as Hamiltonian reductions of the affine closure of the cotangent bundle of base affine space for suitable choices of stability parameter of a maximal torus. We also realize the base change of the universal Poisson deformation of each of these crepant projective partial resolutions as the GIT quotient of the affine closure of the cotangent bundle of base affine space at the same stability parameter.
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BibTeX
@misc{bellamy2026crepant,
title = {{Crepant partial resolutions of the nilpotent cone via Hamiltonian reduction}},
author = {Gwyn Bellamy and Tom Gannon},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.25994},
eprint = {2608.25994},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.25994},
}
RIS
TY - UNPB
TI - Crepant partial resolutions of the nilpotent cone via Hamiltonian reduction
AU - Gwyn Bellamy
AU - Tom Gannon
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2608.25994
UR - https://arxiv.org/abs/2608.25994
AB - We show that the nilpotent cone associated to a simply connected semisimple algebraic group, together with all its crepant projective partial resolutions, can be constructed as Hamiltonian reductions of the affine closure of the cotangent bundle of base affine space for suitable choices of stability parameter of a maximal torus. We also realize the base change of the universal Poisson deformation of each of these crepant projective partial resolutions as the GIT quotient of the affine closure of the cotangent bundle of base affine space at the same stability parameter.
ER -