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Actions of groups of birationally extendible automorphisms. (English) Zbl 0943.32014
Noguchi, J. (ed.) et al., Geometric complex analysis. Proceedings of the conference held at the 3rd International Research Institute of the Mathematical Society of Japan, Hayama, March 19-29, 1995. Singapore: World Scientific. 261-285 (1996).
The authors mainly study the algebraic properties of group actions on bounded domains in \(\mathbb{C}^n\). A typical result is the following: Let \(V\) be a projective variety, \(D\subset V\) a domain and \(G\) a Lie group of birationally extendible automorphisms of \(D\). Suppose that \(G\) has finitely many components. Then there exist an algebraic extension of \(G\), i.e., a homomorphism of \(G\) into a complex algebraic group \(\widetilde G\), and an algebraic variety \(X\) birationally equivalent to \(G\) such that \(D\) embeds biregularly into \(X\) and the action of \(G\) becomes regular.
The authors also give conditions for semialgebraically defined domains \(D\) in \(V\) such that the above result applies. These conditions are formulated in the spirit of results of S. M. Webster [Invent. Math. 43, No. 1, 53-68 (1977; Zbl 0355.32026)].
For the entire collection see [Zbl 0903.00037].

32M05 Complex Lie groups, group actions on complex spaces
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