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

 

Separated $ G\sb{a}$-actions


Author: Andy R. Magid
Journal: Proc. Amer. Math. Soc. 76 (1979), 35-38
MSC: Primary 14L30; Secondary 14D25
MathSciNet review: 534385
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Abstract: Let X be an open subvariety of an affine variety, i.e. a quasi-affine variety, over an algebraically closed field, and suppose the additive algebraic group $ {G_a}$ acts on X. Then a geometric quotient of X by $ {G_a}$ exists if and only if every point x of X has a $ {G_a}$-stable open neighborhood U such that the morphism $ {G_a} \times U \to U \times U$ which sends (t, u) to (tu, u) has closed image and finite fibres.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0534385-1
PII: S 0002-9939(1979)0534385-1
Article copyright: © Copyright 1979 American Mathematical Society