On actions of ℂ * on algebraic spaces
Bialynicki-Birula, Andrzej
Annales de l'Institut Fourier, Tome 43 (1993), p. 359-364 / Harvested from Numdam
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Le résultat principal de cet article est la constatation que tous les points schématiques de la source d’une action de C * sur un espace algébrique X sont schématiques sur X.

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.

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     author = {Bialynicki-Birula, Andrzej},
     title = {On actions of ${\mathbb {C}}^*$ on algebraic spaces},
     journal = {Annales de l'Institut Fourier},
     volume = {43},
     year = {1993},
     pages = {359-364},
     doi = {10.5802/aif.1335},
     mrnumber = {94c:14040},
     zbl = {0779.14014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1993__43_2_359_0}
}

Bialynicki-Birula, Andrzej. On actions of ${\mathbb {C}}^*$ on algebraic spaces. Annales de l'Institut Fourier, Tome 43 (1993) pp. 359-364. doi : 10.5802/aif.1335. http://gdmltest.u-ga.fr/item/AIF_1993__43_2_359_0/

[B-BS] A. Bialynicki-Birula, A. Sommese, Quotients by C* and Sl(2) actions, Trans. Amer. Math. Soc., 279 (1983), 773-800. | MR 85i:32045 | Zbl 0566.32026

[Ka] W. Kaup, Reele Transformationsgruppen und invariante Metriken auf komplexen Raumen, Invent. Math., 3 (1967), 43-70. | MR 35 #6865 | Zbl 0157.13401

[Kn] D. Knutson, Algebraic spaces, Lecture Notes in Mathematics, 203, (1971), Springer-Verlag. | MR 46 #1791 | Zbl 0221.14001

[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. | MR 92k:32048 | Zbl 0774.14001

[GIT] D. Mumford, J. Fogarty, Geometric Invariant Theory, 2nd edition, Ergeb. Math. 36, Springer-Verlag, 1982. | Zbl 0504.14008

[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. | Zbl 0186.26205

[Se1] J.-P. Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier, 6 (1955-1956), 1-42. | Numdam | MR 18,511a | Zbl 0075.30401

[Se2] J.-P. Serre, Espaces fibrés algébriques in Anneaux de Chow et Applications, Séminaire Chevalley, E.N.S. Paris, 1958. | Numdam

[Su] H. Sumihiro, Equivariant completions I, J. Math. Kyoto Univ., 14 (1974), 1-28. | MR 49 #2732 | Zbl 0277.14008