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Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 3, Pages 5–22 (Mi izv2759)  

This article is cited in 1 scientific paper (total in 1 paper)

Projective embeddings of homogeneous spaces with small boundary

I. V. Arzhantsev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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: algebraic group, homogeneous space, epimorphic subgroup, Cox ring.

DOI: https://doi.org/10.4213/im2759

Full text: PDF file (551 kB)
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English version:
Izvestiya: Mathematics, 2009, 73:3, 437–453

Bibliographic databases:

UDC: 512.745.2
MSC: 14L24, 14L30, 14M17
Received: 11.01.2008
Revised: 31.08.2008

Citation: I. V. Arzhantsev, “Projective embeddings of homogeneous spaces with small boundary”, Izv. RAN. Ser. Mat., 73:3 (2009), 5–22; Izv. Math., 73:3 (2009), 437–453

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Avdeev R., “An epimorphic subgroup arising from Roberts' counterexample”, Indag. Math. (N.S.), 23:1-2 (2012), 10–18  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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