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- W2078437137 abstract "The author considers an algebraic action of a connected reductive algebraic group defined over an algebraically closed field on an affine irreducible algebraic variety , and studies the question of when the action of a Borel subgroup of on is stable, i.e., the -orbit of any point belonging to some nonempty open subset of is closed in . A criterion for stability is obtained: Suppose that . In order that the action of on be stable it is necessary, and, if is semisimple and the group of divisor classes is periodic, also sufficient that contain a point with a finite -stabilizer. For an action defined by a linear representation the cases when is not stable and either is simple or is semisimple and the action is irreducible are listed. A general criterion for an orbit of a connected solvable group acting on an affine variety to be closed is also obtained, and it is used to obtain a simple sufficient condition for an orbit of such a group, acting linearly, to be closed.Bibliography: 30 titles." @default.
- W2078437137 created "2016-06-24" @default.
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- W2078437137 date "1989-02-28" @default.
- W2078437137 modified "2023-10-11" @default.
- W2078437137 title "CLOSED ORBITS OF BOREL SUBGROUPS" @default.
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- W2078437137 doi "https://doi.org/10.1070/sm1989v063n02abeh003280" @default.
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