Deveney, James K.; Finston, David R. A proper \(G_ a\) action on \(\mathbb{C}^ 5\) which is not locally trivial. (English) Zbl 0832.14036 Proc. Am. Math. Soc. 123, No. 3, 651-655 (1995). Let \(G_a\) denote the additive group of the field of complex numbers \(\mathbb{C}\). The quotient of a proper holomorphic \(G_a\) action on \(\mathbb{C}^n\) is known to carry the structure of a complex analytic manifold, and in the case of a rational algebraic action, the geometric quotient exists as an algebraic space. An example of a proper rational algebraic action on \(\mathbb{C}^5\) is given, where the quotient is not a variety, and therefore the action is not locally trivial in the Zariski topology. Reviewer: Li Fuan (Beijing) Cited in 3 ReviewsCited in 5 Documents MSC: 14L30 Group actions on varieties or schemes (quotients) 14M17 Homogeneous spaces and generalizations 20G20 Linear algebraic groups over the reals, the complexes, the quaternions Keywords:locally trivial action; quotient of holomorphic action; proper rational algebraic action PDFBibTeX XMLCite \textit{J. K. Deveney} and \textit{D. R. Finston}, Proc. Am. Math. Soc. 123, No. 3, 651--655 (1995; Zbl 0832.14036) Full Text: DOI