# On complete orbit spaces of SL(2) actions, II

Andrzej Białynicki-Birula; Joanna Święcicka

Colloquium Mathematicae (1992)

- Volume: 63, Issue: 1, page 9-20
- ISSN: 0010-1354

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topBiałynicki-Birula, Andrzej, and Święcicka, Joanna. "On complete orbit spaces of SL(2) actions, II." Colloquium Mathematicae 63.1 (1992): 9-20. <http://eudml.org/doc/210138>.

@article{Białynicki1992,

abstract = {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.},

author = {Białynicki-Birula, Andrzej, Święcicka, Joanna},

journal = {Colloquium Mathematicae},

keywords = {SL(2); good quotients; action of a reductive group},

language = {eng},

number = {1},

pages = {9-20},

title = {On complete orbit spaces of SL(2) actions, II},

url = {http://eudml.org/doc/210138},

volume = {63},

year = {1992},

}

TY - JOUR

AU - Białynicki-Birula, Andrzej

AU - Święcicka, Joanna

TI - On complete orbit spaces of SL(2) actions, II

JO - Colloquium Mathematicae

PY - 1992

VL - 63

IS - 1

SP - 9

EP - 20

AB - 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.

LA - eng

KW - SL(2); good quotients; action of a reductive group

UR - http://eudml.org/doc/210138

ER -

## References

top- [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.
- [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.
- [BB-Ś2] A. Białynicki-Birula and J. Święcicka, On complete orbit spaces of SL(2)-actions, Colloq. Math. 55 (1988), 229-243. Zbl0682.14034
- [BB-Ś3] A. Białynicki-Birula and J. Święcicka, Good quotients for actions of SL(2), Bull. Polish Acad. Sci. Math. 36 (1988), 375-381. Zbl0780.14024
- [BB-Ś4] A. Białynicki-Birula and J. Święcicka, A reduction theorem for existence of good quotients, Amer. J. Math. 113 (1991), 189-201. Zbl0741.14031
- [C-S] J. Carrell and A. J. Sommese, SL(2,ℂ) actions on compact Kaehler manifolds, Trans. Amer. Math. Soc. 276 (1983), 165-179.
- [K] D. Knutson, Algebraic Spaces, Lecture Notes in Math. 203, Springer, 1971. Zbl0221.14001
- [L] D. Luna, Slices étale, Bull. Soc. Math. France Mém. 33 (1973), 81-105. Zbl0286.14014
- [GIT] D. Mumford, Geometric Invariant Theory, Ergeb. Math. Grenzgeb. 34, Springer, 1982.
- [S] H. Sumihiro, Equivariant completions, J. Math. Kyoto Univ. 14 (1974), 1-28.

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