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References
[A] Atiyah, M.: Convexity and commuting Hamiltonians. Bull. Lond. Math. Soc.14, 1–15 (1982)
[D-H] Duistermaat, J.J., Heckman, G.: On the variation of cohomology of the symplectic form on the reduced phase space. Invent. Math.69, 259–268 (1982)
[G] Gromov, M.: Pseudoholomorphic curves in symplectic manifolds. Invent. Math.82, 307–347 (1985)
[G-N] Gotay, M., Nester, J.: Pre-symplectic manifolds and the Dirac-Bergmann theory of constraints. J. Math. Phys.19, 2388–2399 (1978)
[G-S]1 Guillemin, V., Sternberg, S.: Convexity properties of the moment map. Invent. Math.67, 491–513 (1982)
[G-S]2 Guillemin, V., Sternberg, S.: Geometric quantization and multiplicities of group representations. Invent. Math.67, 515–538 (1982)
[G-S]3 Guillemin, V., Sternberg, S.: Symplectic Techniques in Physics. Cambridge Univ. Press 1984
[H] Heckman, G.: Thesis. University of Leiden 1980
[Hi] Hirzebruch, F.: The signature of ramified coverings. Lecture given at the Summer Institute on Global Analysis, AMS Berkeley, July, 1968. Symposium in honor of K. Kodaira, D.C. Spencer (ed.). AMS Pub. Providence, 1970
[K-K-S] Kazhdan, D., Kostant, B., Sternberg, S.: Hamiltonian group actions and dynamical systems of Calogero type. Commun. Pure Appl. Math.31, 481–508 (1978)
[Kir] Kirwan, F.: Cohomology of quotients in symplectic and algebraic geometry. Princeton Univ. Press, Princeton, N.J. 1984
[Kod] Kodaira, K.: Complex manifolds and deformations of complex structures. Berlin-Heidelberg-New York: Springer 1986
[Kos] Kostant, D.: A formula for the multiplicity of a weight. Trans. Am. Math. Soc.93, 53–73 (1959)
[M]1 MacDuff, D.: Examples of simply connected non-Kahlerian manifolds. J. Differ. Geom.20, 267–277 (1984)
[M]2 MacDuff, D.: Examples of symplectic structures. Preprint, SUNY Stony Brook 1986
[Mel] Melrose, R.: Analysis on manifolds with corners. MIT 1988
[M-F] Mumford, D., Fogarty, J.: Geometric invariant theory. Berlin-Heidelberg-New York: Springer 1982
[N] Ness, L.: A stratification of the null cone via the moment map. Am. J. Math.106, 1281–1325 (1984)
[S] Sternberg, S.: On minimal coupling and the symplectic mechanics of a classical particle in the presence of a Yang-Mills field., Proc. Natl. Acad. Sci. USA74, 5253–5254 (1977)
[W]1 Weinstein, A.: Lectures on Symplectic manifolds. CBMS Reg. Conf. Ser. Math., Vol. 29. AMS Providence, R.I. 1977
[W]2 Weinstein, A.: Fat bundles and symplectic manifolds. Adv. Math.37, 239–250 (1980)
[Z] Zhelobenko, D.P.: Compact Lie groups and their representations. AMS Transl., Vol. 40. AMS, Providence, R.I. 1972
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Guillemin, V., Sternberg, S. Birational equivalence in the symplectic category. Invent Math 97, 485–522 (1989). https://doi.org/10.1007/BF01388888
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DOI: https://doi.org/10.1007/BF01388888