The aim of this paper is to extend the results of [BB-Ś2] concerning geometric quotients of actions of SL(2) to the case of good quotients. Thus the results of the present paper can be applied to any action of SL(2) on a complete smooth algebraic variety, while the theorems proved in [BB-Ś2] concerned only special situations.
@article{bwmeta1.element.bwnjournal-article-cmv63i1p9bwm, author = {Andrzej Bia\l ynicki-Birula and Joanna \'Swi\k ecicka}, title = {On complete orbit spaces of SL(2) actions, II}, journal = {Colloquium Mathematicae}, volume = {63}, year = {1992}, pages = {9-20}, zbl = {0813.14032}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv63i1p9bwm} }
Białynicki-Birula, Andrzej; Święcicka, Joanna. On complete orbit spaces of SL(2) actions, II. Colloquium Mathematicae, Tome 63 (1992) pp. 9-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv63i1p9bwm/
[000] [BB-S] A. Białynicki-Birula and A. J. Sommese, Quotients by ℂ* and SL(2,ℂ) actions, Trans. Amer. Math. Soc. 279 (1983), 773-800.
[001] [BB-Ś1] A. Białynicki-Birula and J. Święcicka, Complete quotients by algebraic torus actions, in: Group Actions and Vector Fields, Lecture Notes in Math. 956, Springer, 1981, 10-22.
[002] [BB-Ś2] A. Białynicki-Birula and J. Święcicka, On complete orbit spaces of SL(2)-actions, Colloq. Math. 55 (1988), 229-243. | Zbl 0682.14034
[003] [BB-Ś3] A. Białynicki-Birula and J. Święcicka, Good quotients for actions of SL(2), Bull. Polish Acad. Sci. Math. 36 (1988), 375-381. | Zbl 0780.14024
[004] [BB-Ś4] A. Białynicki-Birula and J. Święcicka, A reduction theorem for existence of good quotients, Amer. J. Math. 113 (1991), 189-201. | Zbl 0741.14031
[005] [C-S] J. Carrell and A. J. Sommese, SL(2,ℂ) actions on compact Kaehler manifolds, Trans. Amer. Math. Soc. 276 (1983), 165-179.
[006] [K] D. Knutson, Algebraic Spaces, Lecture Notes in Math. 203, Springer, 1971. | Zbl 0221.14001
[007] [L] D. Luna, Slices étale, Bull. Soc. Math. France Mém. 33 (1973), 81-105. | Zbl 0286.14014
[008] [GIT] D. Mumford, Geometric Invariant Theory, Ergeb. Math. Grenzgeb. 34, Springer, 1982.
[009] [S] H. Sumihiro, Equivariant completions, J. Math. Kyoto Univ. 14 (1974), 1-28.