Convexity of moment polytopes of algebraic varieties

Liu, William

doi:10.1090/S0002-9939-03-07120-X

Convexity of moment polytopes of algebraic varieties
HTML articles powered by AMS MathViewer

by William Liu PDF

Proc. Amer. Math. Soc. 131 (2003), 2921-2932 Request permission

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