|
A convexity theorem for the real part of a Borel invariant subvariety
Author(s):
Timothy
E.
Goldberg
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1447-1458.
MSC (2000):
Primary 53D20;
Secondary 14L24, 53C55
Posted:
November 10, 2008
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
M. Brion proved a convexity result for the moment map image of an irreducible subvariety of a compact integral Kähler manifold preserved by the complexification of the Hamiltonian group action. V. Guillemin and R. Sjamaar generalized this result to irreducible subvarieties preserved only by a Borel subgroup. In another direction, L. O'Shea and R. Sjamaar proved a convexity result for the moment map image of the submanifold fixed by an antisymplectic involution. Analogous to Guillemin and Sjamaar's generalization of Brion's theorem, in this paper we generalize O'Shea and Sjamaar's result, proving a convexity theorem for the moment map image of the involution fixed set of an irreducible subvariety preserved by a Borel subgroup.
References:
-
- 1.
- Jeffrey Adams, Parameters for representations of real groups, notes from the AIM workshop, Palo Alto, July 2005, available at http://atlas.math.umd.edu/papers/summer05/parameters.pdf.
- 2.
- Michel Brion, Sur l'image de l'application moment, Séminaire d'algèbre Paul Dubreil et Marie-Paule Malliavin (Paris, 1986) (M.-P. Malliavin, ed.), Lecture Notes in Mathematics, vol. 1296, Springer-Verlag, Berlin, 1987, pp. 177-192. MR 932055 (89i:32062)
- 3.
- J. J. Duistermaat and J. A. C. Kolk, Lie Groups, Springer, Berlin, 2000. MR 1738431 (2001j:22008)
- 4.
- Victor Guillemin and Reyer Sjamaar, Convexity theorems for varieties invariant under a Borel subgroup, Pure Appl. Math. Q. 2 (2006), no. 3, pp. 637-653. MR 2252111 (2007d:53140)
- 5.
- Victor Guillemin and Shlomo Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982), no. 3, 491-513. MR 664117 (83m:58037)
- 6.
- Frances Kirwan, Convexity properties of the moment mapping, III, Invent. Math. 77 (1984), no. 3, 547-552. MR 759257 (86b:58042b)
- 7.
- Bertrand Kostant, Quantization and unitary representations. I. Prequantization, Lectures in Modern Analysis and Applications, III (Washington, D.C.) (C. T. Taam, ed.), Lecture Notes in Mathematics, vol. 170, Springer-Verlag, Berlin, 1970, pp. 87-208. MR 0294568 (45:3638)
- 8.
- David Mumford, The Red Book of Varieties and Schemes, volume 1358 of Lecture Notes in Mathematics, expanded second edition, Springer-Verlag, Berlin, 1999. MR 1748380 (2001b:14001)
- 9.
- Luis O'Shea and Reyer Sjamaar, Moment maps and Riemannian symmetric pairs, Math. Ann. 317 (2000), 415-457. MR 1776111 (2001g:53146)
- 10.
- Raymond O. Wells, Jr., Differential Analysis on Complex Manifolds, third edition, Springer-Verlag, New York, 2008. MR 2359489 (2008g:32001)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
53D20,
14L24, 53C55
Retrieve articles in all Journals with MSC
(2000):
53D20,
14L24, 53C55
Additional Information:
Timothy
E.
Goldberg
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14850-4201
Email:
goldberg@math.cornell.edu
DOI:
10.1090/S0002-9939-08-09764-5
PII:
S 0002-9939(08)09764-5
Received by editor(s):
January 15, 2008
Posted:
November 10, 2008
Additional Notes:
The author was partially supported by National Science Foundation Grant DMS-0300172.
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org