# A recipe for finding open subsets of vector spaces with a good quotient

A. BiaŁynicki-Birula; J. Święcicka

Colloquium Mathematicae (1998)

- Volume: 77, Issue: 1, page 97-114
- ISSN: 0010-1354

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topBiaŁynicki-Birula, A., and Święcicka, J.. "A recipe for finding open subsets of vector spaces with a good quotient." Colloquium Mathematicae 77.1 (1998): 97-114. <http://eudml.org/doc/210579>.

@article{BiaŁynicki1998,

author = {BiaŁynicki-Birula, A., Święcicka, J.},

journal = {Colloquium Mathematicae},

keywords = {group actions; algebraic spaces; toric varieties; reductive groups; rational representations; polytopes; maximal invariant open subsets; good quotient},

language = {eng},

number = {1},

pages = {97-114},

title = {A recipe for finding open subsets of vector spaces with a good quotient},

url = {http://eudml.org/doc/210579},

volume = {77},

year = {1998},

}

TY - JOUR

AU - BiaŁynicki-Birula, A.

AU - Święcicka, J.

TI - A recipe for finding open subsets of vector spaces with a good quotient

JO - Colloquium Mathematicae

PY - 1998

VL - 77

IS - 1

SP - 97

EP - 114

LA - eng

KW - group actions; algebraic spaces; toric varieties; reductive groups; rational representations; polytopes; maximal invariant open subsets; good quotient

UR - http://eudml.org/doc/210579

ER -

## References

top- [BBŚw1] A. Białynicki-Birula and J. Święcicka, A reduction theorem for existence of good quotients, Amer. J. Math. 113 (1990), 189-201. Zbl0741.14031
- [BBŚw2] A. Białynicki-Birula and J. Święcicka,Open subsets in projective spaces with a good quotient by an action of a reductive group, Transformation Groups 1 (1996), 153-186. Zbl0912.14016
- [BBŚw3] A. Białynicki-Birula and J. Święcicka,Open subsets in projective spaces with a good quotient by an action of a reductive group,Three theorems on existence of good quotients, Math. Ann. 307 (1997), 143-149. Zbl0870.14034
- [BBŚw4] A. Białynicki-Birula and J. Święcicka,Open subsets in projective spaces with a good quotient by an action of a reductive group,Three theorems on existence of good quotients,A combinatorial approach to geometric invariant theory, in Proc. Sophus Lie Memorial Conf. (Oslo 1992), O. A. Laudal and B. Jahren (eds.), Scand. Univ. Press, Oslo, 115-127.
- [C] D. A. Cox, The homogeneous coordinate ring of a toric variety, J. Algebraic Geom. 4 (1995), 17-50. Zbl0846.14032
- [GIT] D. Mumford, Geometric Invariant Theory, Ergeb. Math. Grenzgeb. 34, Springer, 1982.
- [K] D. Knutson, Algebraic Spaces, Lecture Notes in Math. 203, Springer, 1971. Zbl0221.14001
- [N] M. Nagata, Note on orbit spaces, Osaka Math. J. 14 (1962), 21-31. Zbl0103.38303
- [Oda] T. Oda, Convex Bodies and Algebraic Geometry, Springer, 1985. Zbl0628.52002
- [S] C. S. Seshadri, Quotient spaces modulo reductive algebraic groups, Ann. of Math. 95 (1972), 511-556. Zbl0241.14024

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