On embeddings of homogeneous spaces with small boundary

Ivan V. Arzhantsev; Juergen Hausen

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On embeddings of homogeneous spaces with small boundary

Ivan V. Arzhantsev·Juergen Hausen

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Abstract

We study equivariant embeddings with small boundary of a given homogeneous space $G/H$, where $G$ is a connected, linear algebraic group with trivial Picard group and only trivial characters, and $H \subset G$ is an extension of a connected Grosshans subgroup by a torus. Under certain maximality conditions, like completeness, we obtain finiteness of the number of isomorphism classes of such embeddings, and we provide a combinatorial description the embbeddings and their morphisms. The latter allows a systematic treatment of examples and basic statements on the geometry of the equivariant embeddings of a given homogeneous space $G/H$.

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Ivan V. Arzhantsev, Juergen Hausen. 2005-10-20. On embeddings of homogeneous spaces with small boundary. https://arxiv.org/abs/math/0507557

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