On actions of * on algebraic spaces

Andrzej Bialynicki-Birula

Annales de l'institut Fourier (1993)

  • Volume: 43, Issue: 2, page 359-364
  • ISSN: 0373-0956

Abstract

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The main result of the paper says that all schematic points of the source of an action of C * on an algebraic space X are schematic on X .

How to cite

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Bialynicki-Birula, Andrzej. "On actions of ${\mathbb {C}}^*$ on algebraic spaces." Annales de l'institut Fourier 43.2 (1993): 359-364. <http://eudml.org/doc/74999>.

@article{Bialynicki1993,
abstract = {The main result of the paper says that all schematic points of the source of an action of $C^*$ on an algebraic space $X$ are schematic on $X$.},
author = {Bialynicki-Birula, Andrzej},
journal = {Annales de l'institut Fourier},
keywords = {algebraic spaces; toric varieties; action of },
language = {eng},
number = {2},
pages = {359-364},
publisher = {Association des Annales de l'Institut Fourier},
title = {On actions of $\{\mathbb \{C\}\}^*$ on algebraic spaces},
url = {http://eudml.org/doc/74999},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Bialynicki-Birula, Andrzej
TI - On actions of ${\mathbb {C}}^*$ on algebraic spaces
JO - Annales de l'institut Fourier
PY - 1993
PB - Association des Annales de l'Institut Fourier
VL - 43
IS - 2
SP - 359
EP - 364
AB - The main result of the paper says that all schematic points of the source of an action of $C^*$ on an algebraic space $X$ are schematic on $X$.
LA - eng
KW - algebraic spaces; toric varieties; action of
UR - http://eudml.org/doc/74999
ER -

References

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  1. [B-BS] A. BIALYNICKI-BIRULA, A. SOMMESE, Quotients by C* and Sl(2) actions, Trans. Amer. Math. Soc., 279 (1983), 773-800. Zbl0566.32026MR85i:32045
  2. [Ka] W. KAUP, Reele Transformationsgruppen und invariante Metriken auf komplexen Raumen, Invent. Math., 3 (1967), 43-70. Zbl0157.13401MR35 #6865
  3. [Kn] D. KNUTSON, Algebraic spaces, Lecture Notes in Mathematics, 203, (1971), Springer-Verlag. Zbl0221.14001MR46 #1791
  4. [L] D. LUNA, Toute variété de Moisezon presque homogène sous un tore est un schéma, C.R. Acad. Sci. Paris, 314, Série I, (1992), 65-67. Zbl0774.14001MR92k:32048
  5. [GIT] D. MUMFORD, J. FOGARTY, Geometric Invariant Theory, 2nd edition, Ergeb. Math. 36, Springer-Verlag, 1982. Zbl0504.14008
  6. [M] B.G. MOISEZON, Resolution theorems for compact complex spaces with a sufficiently large field of meromorphic functions, Izv. Akad. Nauk SSSR, Ser. Mat., 31 (1967), 1385. Zbl0186.26205
  7. [Se1] J.-P. SERRE, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier, 6 (1955-1956), 1-42. Zbl0075.30401MR18,511a
  8. [Se2] J.-P. SERRE, Espaces fibrés algébriques in Anneaux de Chow et Applications, Séminaire Chevalley, E.N.S. Paris, 1958. 
  9. [Su] H. SUMIHIRO, Equivariant completions I, J. Math. Kyoto Univ., 14 (1974), 1-28. Zbl0277.14008MR49 #2732

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