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arXiv · 2609.04685

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 $Q^3$, or a product $\mathbb{P}^{2m+1-d} \times Y$ with $1 \leq d=\dim Y \leq m$, where $Y$ is a product of cominuscule varieties.

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Cong Ding, Baohua Fu, Zhijun Luo. 2026-09-04. Heisenberg Equivariant Compactifications of Rational Homogeneous Varieties. https://arxiv.org/abs/2609.04685

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