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Heisenberg Equivariant Compactifications of Rational Homogeneous Varieties

  • Cong Ding
  • Baohua Fu
  • Zhijun Luo
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Abstract

Let G/P be a complex projective rational homogeneous variety of dimension 2m+1. We prove that G/P is an equivariant compactification of the Heisenberg group of dimension 2m+1 if and only if it is isomorphic to either an adjoint variety, or the 3-dimensional smooth quadric Q3, or a product ℙ2m+1−d × Y with 1 ≤ d=dim Y ≤ m, where Y is a product of cominuscule varieties.

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Cite

BibTeXRIS
BibTeX
@misc{ding2026heisenberg,
  title = {{Heisenberg Equivariant Compactifications of Rational Homogeneous Varieties}},
  author = {Cong Ding and Baohua Fu and Zhijun Luo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04685},
  eprint = {2609.04685},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04685},
}
RIS
TY  - UNPB
TI  - Heisenberg Equivariant Compactifications of Rational Homogeneous Varieties
AU  - Cong Ding
AU  - Baohua Fu
AU  - Zhijun Luo
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.04685
UR  - https://arxiv.org/abs/2609.04685
AB  - Let G/P be a complex projective rational homogeneous variety of dimension 2m+1. We prove that G/P is an equivariant compactification of the Heisenberg group of dimension 2m+1 if and only if it is isomorphic to either an adjoint variety, or the 3-dimensional smooth quadric Q^3, or a product ℙ^2m+1−d × Y with 1 ≤ d=dim Y ≤ m, where Y is a product of cominuscule varieties.
ER  -