Mathematical Research Letters
Volume 3, Issue 5, September 1996 pp. 619-627.
Equivariant Affine Line Bundles and LinearizationAuthors: Hanspeter Kraft and Frank Kutzschebauch
Author institution: Universität Basel
Summary: We show that every algebraic action of a linearly reductive group on affine $n$-space ${\Bbb C}^n$ which is given by {Jonquière} automorphisms is linearizable. Similarly, every holomorphic action of a compact group $K$ by (holomorphic) {Jonquière} automorphisms is linearizable. Moreover, any holomorphic action of $K$ on ${\Bbb C}^2$ by overshears is linearizable, too. These results are based on the fact that equivariant algebraic or holomorphic affine line bundles over ${\Bbb C}^n$ are trivial.
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