Geodesic
Projective embeddings of homogeneous spaces with small boundary
Izvestiya. Mathematics , Tome 73 (2009) no. 3, pp. 437-453

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We study open equivariant projective embeddings of homogeneous spaces such that the complement of the open orbit has codimension at least 2. We establish a criterion for the existence of such an embedding, prove that the set of isomorphism classes of such embeddings is finite, and give a construction of the embeddings in terms of Geometric Invariant Theory. A generalization of Cox's construction and the theory of bunched rings enable us to describe in combinatorial terms the basic geometric properties of embeddings with small boundary.
Keywords: homogeneous space, epimorphic subgroup, Cox ring.
Mots-clés : algebraic group 
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     author = {I. V. Arzhantsev},
     title = {Projective embeddings of homogeneous spaces with small boundary},
     journal = {Izvestiya. Mathematics },
     pages = {437--453},
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     volume = {73},
     number = {3},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2009_73_3_a1/}
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I. V. Arzhantsev. Projective embeddings of homogeneous spaces with small boundary. Izvestiya. Mathematics , Tome 73 (2009) no. 3, pp. 437-453. http://geodesic.mathdoc.fr/item/IM2_2009_73_3_a1/