Separated $G_{a}$-actions
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- by Andy R. Magid PDF
- Proc. Amer. Math. Soc. 76 (1979), 35-38 Request permission
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.References
- Amassa Fauntleroy and Andy R. Magid, Proper $G_{a}$-actions, Duke Math. J. 43 (1976), no. 4, 723–729. MR 417196
- Amassa Fauntleroy and Andy R. Magid, Quasi-affine surfaces with $G_{a}$-actions, Proc. Amer. Math. Soc. 68 (1978), no. 3, 265–270. MR 472839, DOI 10.1090/S0002-9939-1978-0472839-6
- David Mumford, Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 34, Springer-Verlag, Berlin-New York, 1965. MR 0214602, DOI 10.1007/978-3-662-00095-3
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 76 (1979), 35-38
- MSC: Primary 14L30; Secondary 14D25
- DOI: https://doi.org/10.1090/S0002-9939-1979-0534385-1
- MathSciNet review: 534385