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Torus actions on weakly pseudoconvex spaces
Author(s):
Stefano
Trapani
Journal:
Trans. Amer. Math. Soc.
358
(2006),
1971-1981.
MSC (2000):
Primary 32M05, 32U10
Posted:
December 20, 2005
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Abstract:
We show that the univalent local actions of the complexification of a compact connected Lie group  on a weakly pseudoconvex space where  is acting holomorphically have a universal orbit convex weakly pseudoconvex complexification. We also show that if  is a torus, then every holomorphic action of  on a weakly pseudoconvex space extends to a univalent local action of 
References:
-
- 1.
- E. Casadio Tarabusi, A. Iannuzzi, S. Trapani, Globalizations, fiber bundles and envelopes of holomorphy Math Z. 233 (2000) pag. 535-551. MR 1750936 (2001f:32035)
- 2.
- M. Coltoiu, N. Mihalache, Strongly plurisubharmonic exhaustion functions on 1-convex spaces Math. Ann. 270 (1985), pag. 63-68. MR 0769607 (86a:32037)
- 3.
- J. P. Demailly, Estimations
 pour l'operate'ur  d'un fibre' vectoriel holomorphe semi-positif au dessus d'une variete' Kaelerienne complete Ann. Sci. Ecole Norm. Sup. 15 (1982) pag. 457-511. MR 0690650 (85d:32057) - 4.
- J. P. Demailly, Singular Hermitian metrics on positive line bundles in ``Complex algebraic varieties" Bayreuth 1990 (K. Hulek et al., eds.), Lecture Notes in Math. vol. 1507 Springer Berlin (1992) 361-409. MR 1178721 (93g:32044)
- 5.
- J. E. Fornaess, R. Narashimhan, The Levi problem on complex spaces with singularities Math. Ann. 248 (1980) pag. 47-72. MR 0569410 (81f:32020)
- 6.
- H. Grauert, Bemerkenswerte pseudokonvexe Mannigfaltigkeiten Math Z. 81 (1963) pgs. 377-391. MR 0168798 (29:6054)
- 7.
- P. Heinzner, Geometric invariant theory of Stein Spaces Math. Ann. 289 (1991) pag. 631-662. MR 1103041 (92j:32116)
- 8.
- P. Heinzner, Equivariant holomorphic extension of real analytic manifolds Bull. Soc. Math. France 121 (1993) pag. 445-463. MR 1242639 (94i:32050)
- 9.
- P. Heinzner, The minimum principle from an Hamiltonian point of view Doc. Math. 3 (1998) pag. 1-14 (electronic) MR 1620612 (99c:32044)
- 10.
- P. Heinzner, A. Huckleberry, F. Loose, Kahlerian extension of the symplectic reductions J. Reine Angew. Math. 455 (1994) pag. 123-140. MR 1293876 (95k:58061)
- 11.
- P. Heinzner, A. Iannuzzi, Integration of local actions on holomorphic fiber spaces Nagoja Math. J. 146 (1997) pag. 31-53. MR 1460953 (98k:32047)
- 12.
- G. Hochschild, The structure of Lie groups Holden-Day, San Francisco, London, Amsterdam (1965) MR 0207883 (34:7696)
- 13.
- A. Iannuzzi, Induced local actions on taut and Stein manifolds preprint.
- 14.
- W. Kaup, Infinitesimale Tranformationengruppen komplexes Math. Ann. 160 (1965) pag. 72-93. MR 0181761 (31:5988)
- 15.
- S. Kobayashi, Hyperbolic complex spaces Springer-Verlag (1998). MR 1635983 (99m:32026)
- 16.
- D. Mumford, J. Fogarty, F. Kirwan, Geometric Invariant theory Springer-Verlag (Third enlarged edition 1994). MR 1304906 (95m:14012)
- 17.
- R. S. Palais, A global formulation of the Lie theory of transformation groups Mem. of the Amer. Math. Soc. (1955). MR 0121424 (22:12162)
- 18.
- Y. T. Siu Holomorphic fiber bundles whose fiber are bounded Stein domains with zero first Betti number Math. Ann. 219 (1976) pgs. 171-192. MR 0390303 (52:11129)
- 19.
- Y. T. Siu Pseudoconvexity and the problem of Levi Bull. Am. Math. Soc. 84 (1978) pgs. 481-512. MR 0477104 (57:16648)
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Additional Information:
Stefano
Trapani
Affiliation:
Dipartimento di Matematica, Universita' di Roma 2 Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, Italy
Email:
trapani@mat.uniroma2.it
DOI:
10.1090/S0002-9947-05-04053-5
PII:
S 0002-9947(05)04053-5
Received by editor(s):
August 7, 2003
Received by editor(s) in revised form:
January 27, 2004
Posted:
December 20, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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