Quasi-affine surfaces with 𝐺ₐ-actions

Fauntleroy, Amassa; Magid, Andy R.

doi:10.1090/S0002-9939-1978-0472839-6

Quasi-affine surfaces with $G_{a}$-actions
HTML articles powered by AMS MathViewer

by Amassa Fauntleroy and Andy R. Magid PDF

Proc. Amer. Math. Soc. 68 (1978), 265-270 Request permission

Abstract:

A normal quasi-affine surface over an algebraically closed field of characteristic zero which has a ${G_a}$-action is shown to have a geometric quotient if and only if the action is without fixed points. If the surface is factorial affine, and the action without fixed points, the surface is the product of a curve and ${G_a}$.

References

Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042
S. U. Chase, D. K. Harrison, and Alex Rosenberg, Galois theory and Galois cohomology of commutative rings, Mem. Amer. Math. Soc. 52 (1965), 15–33. MR 195922
Amassa Fauntleroy and Andy R. Magid, Proper $G_{a}$-actions, Duke Math. J. 43 (1976), no. 4, 723–729. MR 417196
Robert M. Fossum, The divisor class group of a Krull domain, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 74, Springer-Verlag, New York-Heidelberg, 1973. MR 0382254, DOI 10.1007/978-3-642-88405-4
Andy R. Magid, The Picard sequence of a fibration, Brauer groups (Proc. Conf., Northwestern Univ., Evanston, Ill., 1975) Lecture Notes in Math., Vol. 549, Springer, Berlin, 1976, pp. 71–85. MR 0429880
Hideyuki Matsumura, Commutative algebra, W. A. Benjamin, Inc., New York, 1970. MR 0266911
Maxwell Rosenlicht, On quotient varieties and the affine embedding of certain homogeneous spaces, Trans. Amer. Math. Soc. 101 (1961), 211–223. MR 130878, DOI 10.1090/S0002-9947-1961-0130878-0