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A non-triangular action of \({\mathbb{G}}_ a\) on \({\mathbb{A}}^ 3\). (English) Zbl 0555.14019
An automorphism \(f: {\mathbb{C}}^ n\to {\mathbb{C}}^ n,\) \(f(x)=(f_ 1(x),...,f_ n(x))\) is ”triangular” if \(f_ i(x)\) depends only on \(x_ 1,...,x_ i\) \((i=1,...,n)\). A polynomial action of the additive group \({\mathbb{C}}\) on \({\mathbb{C}}^ 3\) is exhibited which cannot be conjugated, by a polynomial automorphism, into triangular form. Such examples do not exist on \({\mathbb{C}}^ 2\).

14L30 Group actions on varieties or schemes (quotients)
32M05 Complex Lie groups, group actions on complex spaces
Full Text: DOI
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