Equivariant compactifications of reductive groups

Details Equivariant compactifications of reductive groups Equivariant compactifications of reductive groups

2002-07-03

arxiv.org/abs/math/0207034v2

Mathematics

Algebraic Geometry

30 pages, AmSLaTeX. Bibliography: 36 items

Scientific paper

We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under the action of the doubled group by left/right multiplications, the local structure in a neighborhood of a closed orbit, and obtain some conditions of normality and smoothness of a compactification. Our methods of research use the theory of equivariant embeddings of spherical homogeneous spaces and of reductive algebraic semigroups.

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