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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Differential forms on quotients by reductive group actions

Author(s): Michel Brion
Journal: Proc. Amer. Math. Soc. 126 (1998), 2535-2539.
MSC (1991): Primary 14L30, 22E99
MathSciNet review: 1451789
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Abstract: Let $X$ be a smooth affine algebraic variety where a reductive algebraic group $G$ acts with a smooth quotient space $Y=X//G$. We show that the algebraic differential forms on $X$ which are pull-backs of forms on $Y$ are exactly the $G$-invariant horizontal differential forms on $X$.

References:

[B]
M. Brion: Sur les modules de covariants, Ann. scient. Éc. Norm. Sup. 26 (1993), p. 1-21. MR 95c:14062

[H]
R. Hartshorne: Stable reflexive sheaves, Math. Ann. 254 (1980), p. 121-176. MR 82b:14011

[K]
E. Kunz: Kähler Differentials, Viehweg, Braunschweig-Wiesbaden, 1986.MR 88e:14025

[L1]
D. Luna: Slices étales, Bull. Soc. math. France, Mémoire 33 (1973), p. 81-105. MR 49:7269

[L2]
D. Luna: Adhérences d'orbites et invariants, Invent. Math. 29 (1975), 231-238. MR 51:12879

[L-R]
D. Luna and R. W. Richardson: A generalization of the Chevalley restriction theorem, Duke Math. J. 46 (1979), p. 487-496. MR 80k:14049

[M1]
Peter W. Michor: Basic differential forms for actions of Lie groups, Proc. Amer. Math. Soc. 124 (1996), p. 1633-1642. MR 96g:57041

[M2]
Peter W. Michor: Basic differential forms for actions of Lie groups II, Proc. Amer. Math. Soc. 125 (1997), 2175-2177. CMP 97:10

[P-V]
V. L. Popov and E. B. Vinberg: Invariant Theory, Encyclopaedia of Mathematical Sciences, Algebraic Geometry IV, vol. 55, Springer-Verlag, Berlin 1994, p. 123-284. MR 92d:14010

[So]
L. Solomon: Invariants of finite reflection groups, Nagoya Math. J. 22 (1963), p. 57-64. MR 27:4872

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Additional Information:

Michel Brion
Affiliation: Institut Fourier, B. P. 74, 38402 Saint-Martin d'Hères Cedex, France
Email: mbrion@fourier.ujf-grenoble.fr

DOI: 10.1090/S0002-9939-98-04320-2
PII: S 0002-9939(98)04320-2
Received by editor(s): October 25, 1996
Received by editor(s) in revised form: January 29, 1997
Communicated by: Roe Goodman
Copyright of article: Copyright 1998, American Mathematical Society




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