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On reductive group actions and fixed points
Author(s):
Minhyong
Kim
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3397-3400.
MSC (1991):
Primary 22E10
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Abstract:
Among analytic actions of reductive groups on projective varieties, we characterize the algebraic ones by the existence of fixed points for one-parameter subgroups. This applies to the problem of lifting the action of a compact Lie group on a projective manifold to a line bundle.
References:
- 1.
- M. F. Atiyah, Convexity and commuting Hamiltonians, Bull. Lond. Math. Soc. 14 (1981), 1-15. MR 83e:53037
- 2.
- S. Bochner and D. Montgomery, Groups on analytic manifolds, Ann. Math. 45, no. 3 (1947), 659-669. MR 9:174f
- 3.
- A. Borel, Linear representations of semi-simple groups, in Proc. Symp. Pure Math. 29 (1975), 421-440, Amer. Math. Soc., Providence, RI. MR 51:8271
- 4.
- T. Frankel, Fixed points on Kaehler manifolds, Ann. of Math. 70 (1959), 1-8.
- 5.
- A. Grothendieck, Techniques de construction et théorèmes d'existence en géométrie algébrique IV, Seminaire Bourbaki 221, (1960/61).
- 6.
- V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982), 515-538. MR 83m:58040
- 7.
- S. Lang, Hyperbolic and Diophantine analysis, Bull. Amer. Math. Soc. 14, no. 2, (1986), 159-205. MR 87h:32051
- 8.
- D. Mumford and J. Fogarty, Geometric Invariant Theory, 2nd ed., Springer Verlag, Berlin-Heidelberg-New York (1982). MR 86a:14006
- 9.
- M. Rosenlicht, Some basic theorems on algebraic groups, Amer. J. Math. 78 (1956), 401-443. MR 18:514a
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Additional Information:
Minhyong
Kim
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Email:
kim@math.arizona.edu
DOI:
10.1090/S0002-9939-98-04346-9
PII:
S 0002-9939(98)04346-9
Received by editor(s):
August 21, 1992
Received by editor(s) in revised form:
February 5, 1997
Communicated by:
Eric M. Friedlander
Copyright of article:
Copyright
1998,
American Mathematical Society
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