Convexity of moment polytopes of algebraic varieties
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- by William Liu
- Proc. Amer. Math. Soc. 131 (2003), 2921-2932
- DOI: https://doi.org/10.1090/S0002-9939-03-07120-X
- Published electronically: April 23, 2003
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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
- M. F. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), no. 1, 1–15. MR 642416, DOI 10.1112/blms/14.1.1
- M. F. Atiyah and A. N. Pressley, Convexity and loop groups, Arithmetic and geometry, Vol. II, Progr. Math., vol. 36, Birkhäuser Boston, Boston, MA, 1983, pp. 33–63. MR 717605
- James B. Carrell and Andrew John Sommese, Some topological aspects of $\textbf {C}^{\ast }$ actions on compact Kaehler manifolds, Comment. Math. Helv. 54 (1979), no. 4, 567–582. MR 552677, DOI 10.1007/BF02566293
- Theodore Frankel, Fixed points and torsion on Kähler manifolds, Ann. of Math. (2) 70 (1959), 1–8. MR 131883, DOI 10.2307/1969889
- V. Guillemin and S. Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982), no. 3, 491–513. MR 664117, DOI 10.1007/BF01398933
- W. Liu, Ph.D thesis, University of Rochester, 1998.
- Stephen A. Mitchell, A filtration of the loops on $\textrm {SU}(n)$ by Schubert varieties, Math. Z. 193 (1986), no. 3, 347–362. MR 862881, DOI 10.1007/BF01229802
- Andrew Pressley and Graeme Segal, Loop groups, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1986. Oxford Science Publications. MR 900587
- Graeme Segal, Loop groups and harmonic maps, Advances in homotopy theory (Cortona, 1988) London Math. Soc. Lecture Note Ser., vol. 139, Cambridge Univ. Press, Cambridge, 1989, pp. 153–164. MR 1055875, DOI 10.1017/CBO9780511662614.015
Bibliographic 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
- Received by editor(s): May 25, 2001
- Published electronically: April 23, 2003
- Communicated by: Mohan Ramachandran
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2921-2932
- MSC (2000): Primary 53D20, 37J15, 58E40; Secondary 22E67, 14M15
- DOI: https://doi.org/10.1090/S0002-9939-03-07120-X
- MathSciNet review: 1974350