Mathematics – Algebraic Geometry
Scientific paper
2005-07-27
J. Algebra, Vol. 304, No. 2, 950-988 (2006)
Mathematics
Algebraic Geometry
minor changes, 30 pages, to appear in J. Algebra
Scientific paper
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 $G/H$.
Arzhantsev Ivan V.
Hausen Juergen
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