发表机构
KAIST（韩国科学技术院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将Cheong关于齐性空间紧化唯一性定理推广至Picard数为一的光滑射影horospherical簇，构造其单幂子群并证明等变紧化的唯一性。
AI 中文摘要
Cheong证明了：若$S$是简单李群且$P$是抛物子群，则当$S/P$不同构于射影空间时，$S/P$在$P$的单幂根$N$的等变紧化在同构意义下是唯一的。我们将此结果推广到Picard数为1的光滑射影horospherical簇$X$上。设$G = \mathrm{Aut}(X)$，$H$为开$G$-轨道中某点的迷向子群。我们描述了$H$的一个单幂子群$N$，当$X$非齐次时，$N$不一定是$H$的单幂根。此外，我们证明了$X$在$N$的等变紧化在同构意义下是唯一的。
英文摘要
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 $G = \mathrm{Aut}(X)$, 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.
Comments15 pages. Comments are welcome!
