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Finite group actions on the non-minimal nilpotent orbit closures in type A

  • Gwyn Bellamy
  • Misha Feigin
  • Pavel Shlykov
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Abstract

We study quotients of the closures of the nilpotent orbits of type A by finite groups of inner automorphisms. Assuming the nilpotent orbit is not minimal, we show that the Q-factorial terminalizations of quotients of nilpotent orbit closures are precisely the quotients of the symplectic resolutions of the orbit closures. This identifies the Mori fan of each Q-factorial terminalization of the quotient with the Mori fan of a symplectic resolution of the orbit closure.

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Cite

BibTeXRIS
BibTeX
@misc{bellamy2026finite,
  title = {{Finite group actions on the non-minimal nilpotent orbit closures in type A}},
  author = {Gwyn Bellamy and Misha Feigin and Pavel Shlykov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37396},
  eprint = {2610.37396},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37396},
}
RIS
TY  - UNPB
TI  - Finite group actions on the non-minimal nilpotent orbit closures in type A
AU  - Gwyn Bellamy
AU  - Misha Feigin
AU  - Pavel Shlykov
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37396
UR  - https://arxiv.org/abs/2610.37396
AB  - We study quotients of the closures of the nilpotent orbits of type A by finite groups of inner automorphisms. Assuming the nilpotent orbit is not minimal, we show that the Q-factorial terminalizations of quotients of nilpotent orbit closures are precisely the quotients of the symplectic resolutions of the orbit closures. This identifies the Mori fan of each Q-factorial terminalization of the quotient with the Mori fan of a symplectic resolution of the orbit closure.
ER  -