On the normality of the closures of spherical orbits (Q1272014)
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scientific article; zbMATH DE number 1226009
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the normality of the closures of spherical orbits |
scientific article; zbMATH DE number 1226009 |
Statements
On the normality of the closures of spherical orbits (English)
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13 June 1999
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Let \(X\) be a normal affine variety acted on by a connected reductive group \(G\) with Borel subgroup \(B\). Suppose that the complexity of the action (that is, the codimension of a generic \(B\)-orbit in \(X)\) is one, and suppose that the categorical quotient of \(X\) by \(G\) is one-dimensional. In this paper it is shown that the closures of all \(G\)-orbits in \(X\) are normal (as was already known for actions of complexity zero).
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normal variety
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orbit closure
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complexity of the action of a reductive group
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