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Projective embeddings of homogeneous spaces with small boundary

By Ivan V. Arzhantsev


We study open equivariant projective embeddings of homogeneous spaces such that the complement of the open orbit does not contain divisors. Criterions of existence of such an embedding are considered and finiteness of isomorphism classes of embeddings for a given homogeneous space is proved. Any embedding with small boundary is realized as a GIT-quotient associated with a linearization of the trivial line bundle on the space of the canonical embedding. The generalized Cox's construction and the theory of bunched rings allow us to describe basic geometric properties of embeddings with small boundary in combinatorial terms.Comment: 15 page

Topics: Mathematics - Algebraic Geometry, Mathematics - Commutative Algebra, 14L24, 14L30, 14M17
Publisher: 'IOP Publishing'
Year: 2008
DOI identifier: 10.1070/IM2009v073n03ABEH002453
OAI identifier:

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