Abstract:We construct four-dimensional symplectic orbifolds admitting Hamiltonian circle actions with isolated fixed points, but not admitting any Hamiltonian action of a two-torus. One example is linear, and one example is compact.
- K. Ahara and A. Hattori, $4$-dimensional symplectic $S^1$-manifolds admitting moment map, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 38 (1991), no. 2, 251–298. MR 1127083
- 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
- Michèle Audin, Hamiltoniens périodiques sur les variétés symplectiques compactes de dimension $4$, Géométrie symplectique et mécanique (La Grande Motte, 1988) Lecture Notes in Math., vol. 1416, Springer, Berlin, 1990, pp. 1–25 (French). MR 1047474, DOI 10.1007/BFb0097462
- 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
- Karshon, Y., Periodic Hamiltonian flows on four–dimensional manifolds, Trans. AMS, submitted. (Available electronically at dg-ga/9510004.)
- Eugene Lerman and Susan Tolman, Hamiltonian torus actions on symplectic orbifolds and toric varieties, Trans. Amer. Math. Soc. 349 (1997), no. 10, 4201–4230. MR 1401525, DOI 10.1090/S0002-9947-97-01821-7
- Tolman, S., Examples of Non-Kaehler Hamiltonian Torus Actions, Invent. Math., to appear.
- S. F. Singer
- Affiliation: Department of Mathematics, Haverford College, Haverford, Pennsylvania 19041
- Email: email@example.com
- J. Talvacchia
- Affiliation: Department of Mathematics, Swarthmore College, Swarthmore, Pennsylvania 19081
- Email: firstname.lastname@example.org
- N. Watson
- Affiliation: Department of Mathematics, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104
- Received by editor(s): July 8, 1997
- Additional Notes: The second author was supported in part by a fellowship from the American Association of University Women and NSF grant DMS 9304580.
- Communicated by: Peter Li
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 937-940
- MSC (1991): Primary 58Fxx
- DOI: https://doi.org/10.1090/S0002-9939-99-04767-X
- MathSciNet review: 1487340