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

Abstract

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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.

How to cite

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Białynicki-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

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  1. [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. 
  2. [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. 
  3. [BB-Ś2] A. Białynicki-Birula and J. Święcicka, On complete orbit spaces of SL(2)-actions, Colloq. Math. 55 (1988), 229-243. Zbl0682.14034
  4. [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
  5. [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
  6. [C-S] J. Carrell and A. J. Sommese, SL(2,ℂ) actions on compact Kaehler manifolds, Trans. Amer. Math. Soc. 276 (1983), 165-179. 
  7. [K] D. Knutson, Algebraic Spaces, Lecture Notes in Math. 203, Springer, 1971. Zbl0221.14001
  8. [L] D. Luna, Slices étale, Bull. Soc. Math. France Mém. 33 (1973), 81-105. Zbl0286.14014
  9. [GIT] D. Mumford, Geometric Invariant Theory, Ergeb. Math. Grenzgeb. 34, Springer, 1982. 
  10. [S] H. Sumihiro, Equivariant completions, J. Math. Kyoto Univ. 14 (1974), 1-28. 

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