Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Convexity of moment polytopes of algebraic varieties

Author(s): William Liu
Journal: Proc. Amer. Math. Soc. 131 (2003), 2921-2932.
MSC (2000): Primary 53D20, 37J15, 58E40; Secondary 22E67, 14M15
Posted: April 23, 2003
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We consider the situation of a compact irreducible subvariety of a smooth compact complex variety equipped with a Kähler form preserved by a torus action. We study the image of that subvariety under the moment map of the Kähler form.

References:

[A]
M.F.Atiyah, Convexity and Commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), 1-15. MR 83e:53037

[A-P]
M.F.Atiyah and A.N.Pressley, Convexity and Loop Groups, Progress in Mathematics 36 (1983), 33-64. MR 85e:22026
[C-S]
James B. Carrell and Andrew J. Sommese, Some Topological Aspects of ${\mathbb C}^{*}$ Actions on Compact Kaehler Manifolds, Comment. Math. Helvetici 54 (1979), 567-582. MR 80m:32032

[F]
T. Frankel, Fixed points and torsion on Kähler manifolds, Annals of Math. 70 (1959), 1-8. MR 24:A1730

[G-S]
V. Guillemin and S. Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982), 491-513. MR 83m:58037

[L]
W. Liu, Ph.D thesis, University of Rochester, 1998.

[M]
S.A.Mitchell, The filtration of the loops on $SU(n)$ by Schubert varieties, Math. Z. 193 (1986), 374-362. MR 88d:32043

[P-S]
A. Pressley and G. Segal, Loop Groups, Oxford Mathematical Monographs, Clarendon Press, 1986. MR 88i:22049

[S]
G.Segal, Loop groups and Harmonic maps, Advances in homotopy theory (Cortona 1988), 153-164, London Math. Soc. Lecture Notes Ser., 139. MR 91m:58043

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53D20, 37J15, 58E40, 22E67, 14M15

Retrieve articles in all Journals with MSC (2000): 53D20, 37J15, 58E40, 22E67, 14M15

Additional Information:

William Liu
Affiliation: Department of Natural and Social Sciences, Bowling Green State University, Firelands College, One University Dr., Huron, Ohio 44839
Email: nwliu@bgnet.bgsu.edu

DOI: 10.1090/S0002-9939-03-07120-X
PII: S 0002-9939(03)07120-X
Keywords: Symplectic structures, Hamiltonian torus action, moment maps, Morse theory, loop groups
Received by editor(s): May 25, 2001
Posted: April 23, 2003
Communicated by: Mohan Ramachandran
Copyright of article: Copyright 2003, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google