Projective embeddings of homogeneous spaces with small boundary

Details Projective embeddings of homogeneous spaces with small boundary Projective embeddings of homogeneous spaces with small boundary

2008-01-13

arxiv.org/abs/0801.1967v1

Izv. Ross. Akad. Nauk Ser. Mat. 73:3 (2009), 5-22; translation in Izvestiya Math. 73:3 (2009), 437-453

Mathematics

Algebraic Geometry

15 pages

Scientific paper

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.

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