Actions of groups of birationally extendible automorphisms

Details Actions of groups of birationally extendible automorphisms Actions of groups of birationally extendible automorphisms

1995-08-22

arxiv.org/abs/alg-geom/9508010v2

Mathematics

Algebraic Geometry

30 pages, AmS-TeX- Version 2.1 (amstex.tex)

Scientific paper

We study the actions of a Lie group $G$ by birationally extendible automorphisms on a domain $D\subset C^n$. For a large class of such domains defined by polynomial inequalities, all automorphisms are of this type. In the cases 1) $G$ has finitely many components or 2) the degree of the automorphisms is bounded, we prove that the action of $G$ is projectively linearizable, i.e. there exist a linear representation of $G$ on some $ C^{N+1}$ and a holomorphic $G$-equivariant embedding $i: D\to P^N$, which is a restriction of a rational mapping. As a corollary we obtain as many rational invariant functions as the dimension of generic orbits allows. A hard copy is available from Dmitri.Zaitsev@rz.ruhr-uni-bochum.de

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