On Hilbert's fourteenth problem for varieties of complexity one. (Q1319337)
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scientific article; zbMATH DE number 549777
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Hilbert's fourteenth problem for varieties of complexity one. |
scientific article; zbMATH DE number 549777 |
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On Hilbert's fourteenth problem for varieties of complexity one. (English)
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2 June 1994
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Let \(G\) be a reductive group and \(B\) a Borel subgroup. The complexity \(c\) of a \(G\)-variety \(X\) is the codimension of a generic \(B\)-orbit. It is shown that the algebra of global functions \(k[X]\) is finitely generated whenever \(c\leq 1\) and \(X\) is unirational. Examples show, that none of the conditions can be relaxed. An application to the Popov-Pommerening conjecture, concerning radical subgroups, is given.
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complexity of \(G\)-variety
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finite generation of the algebra of global functions
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Popov-Pommerening conjecture
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