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PreprintCC BY 4.0arXiv

Equivariant compactifications of a unipotent group by a smooth projective horospherical variety of Picard number one

  • Hyukmoon Choi
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Abstract

Cheong proved that if S is a simple Lie group and P is a parabolic subgroup, then S/P admits a unique equivariant compactification of the unipotent radical N of P, up to isomorphism, provided that S/P is not isomorphic to a projective space. We generalize this result to a smooth projective horospherical variety X with Picard number 1. Let G = Aut(X), and let H be the isotropy subgroup at a point in the open G-orbit. We describe a unipotent subgroup N of H, which is not necessarily the unipotent radical of H when X is not homogeneous. Moreover, we prove that X admits a unique equivariant compactification of N, up to isomorphism.

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Cite

BibTeXRIS
BibTeX
@misc{choi2026equivariant,
  title = {{Equivariant compactifications of a unipotent group by a smooth projective horospherical variety of Picard number one}},
  author = {Hyukmoon Choi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08072},
  eprint = {2609.08072},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08072},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Equivariant compactifications of a unipotent group by a smooth projective horospherical variety of Picard number one
AU  - Hyukmoon Choi
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08072
UR  - https://arxiv.org/abs/2609.08072
AB  - Cheong proved that if S is a simple Lie group and P is a parabolic subgroup, then S/P admits a unique equivariant compactification of the unipotent radical N of P, up to isomorphism, provided that S/P is not isomorphic to a projective space. We generalize this result to a smooth projective horospherical variety X with Picard number 1. Let G = Aut(X), and let H be the isotropy subgroup at a point in the open G-orbit. We describe a unipotent subgroup N of H, which is not necessarily the unipotent radical of H when X is not homogeneous. Moreover, we prove that X admits a unique equivariant compactification of N, up to isomorphism.
ER  -