Algebraic cones (Q845232)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Algebraic cones |
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Algebraic cones (English)
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5 February 2010
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Answering a question of Adjamagbo asked in a letter dated July 9, 2009, the author proofs the following Theorem. Let \(X\) be an irreducible algebraic variety. Then the conditions (i) \(X\) is a cone; (ii) there exists an action of \(M_m\) on \(X\) with a unique fixed point; (iii) there exists an action of \(G_m\) on \(X\) having a fixed point which is a unique closed orbit are related by the implications (i) \(\Rightarrow\) (ii) \(\Rightarrow\) (iii); moreover, if \(X\) is normal, then (iii) \(\Rightarrow\) (i).
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algebraic cone
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monoid action
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group action
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orbit
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action with unique fixed point
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algebra automorphism
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stable ideal
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irreducible algebraic variety
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