Equivariant Affine Line Bundles and Linearization

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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Published 1 January 1996