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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A proper $ {\bf G}\sb a$ action on $ {\bf C}\sp 5$ which is not locally trivial


Authors: James K. Deveney and David R. Finston
Journal: Proc. Amer. Math. Soc. 123 (1995), 651-655
MSC: Primary 14L30; Secondary 14D25
MathSciNet review: 1273487
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Abstract: The quotient of a proper holomorphic $ {G_a}$ action on $ {{\mathbf{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 is given of a proper rational algebraic action for which the quotient is not a variety, and therefore the action is not locally trivial in the Zariski topology.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1273487-0
PII: S 0002-9939(1995)1273487-0
Article copyright: © Copyright 1995 American Mathematical Society