Symplectic subvarieties of projective fibrations over symplectic manifolds
Annales de l'Institut Fourier, Tome 49 (1999) no. 5, pp. 1661-1672.

Soit E→M une fibration symplectique , avec M symplectique et compacte et les fibres projectives complexes; on construit des sous-variétés symplectiques de E analytiques dans la direction verticale, et on donne une application aux fibrés vectoriels complexes sur les variétés symplectiques.

Given a symplectic fibration E→M, with M compact and symplectic and the fibres complex projective, we produce symplectic submanifolds of E analytic in the vertical direction, and apply this to complex vector bundles on symplectic manifolds.

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     title = {Symplectic subvarieties of projective fibrations over symplectic manifolds},
     journal = {Annales de l'Institut Fourier},
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Paoletti, Roberto. Symplectic subvarieties of projective fibrations over symplectic manifolds. Annales de l'Institut Fourier, Tome 49 (1999) no. 5, pp. 1661-1672. doi : 10.5802/aif.1733. https://www.numdam.org/articles/10.5802/aif.1733/

[A] D. Auroux, Asymptotically Holomorphic Families of Symplectic Submanifolds, GAFA, 7 (1997), 29-58. | MR | Zbl

[D] S. Donaldson, Symplectic Submanifolds and Almost Complex Geometry, J. of Diff. Geom., 44 (1996), 666-705. | MR | Zbl

[GLS] V. Guillemin, E. Lerman, S. Sternberg, Symplectic Fibrations and Multiplicity Diagrams, Cambridge University Press, 1996. | MR | Zbl

[GS] V. Guillemin, S. Sternberg, Symplectic Techniques in Physics, Cambridge University Press, 1984. | MR | Zbl

[L] R. Lazarsfeld, Some Applications of the Theory of Ample Vector Bundles, in: Complete Intersections, Acireale 1983, S. Greco and R. Strano eds, Lecture Notes in Mathematics, 1902, Springer Verlag (1984), 29-61. | MR | Zbl

[MS] D. Mcduff, D. Salamon, Introduction to Symplectic Topology, Clarendon Press, Oxford, 1995. | MR | Zbl

[M] D. Mumford, J. Fogarty, F. Kirwan, Geometric Invariant Theory, Springer Verlag, 1994. | MR | Zbl

[S] A. Sommese, Submanifolds of Abelian Varieties, Math. Ann., 233 (1978), 229-256. | MR | Zbl

[W] A. Weinstein, A Universal Phase Space for Particles in a Yang-Mills Field, Lett. Math. Phys., 2 (1977), 417-420. | MR | Zbl

  • Fernández, M.; Muñoz, V.; Ugarte, L. Weakly Lefschetz symplectic manifolds, Transactions of the American Mathematical Society, Volume 359 (2006) no. 4, p. 1851 | DOI:10.1090/s0002-9947-06-04114-6
  • Muñoz, V.; Presas, F.; Sols, I. Almost holomorphic embeddings in Grassmannians with applications to singular symplectic submanifolds, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2002 (2002) no. 547 | DOI:10.1515/crll.2002.048
  • Paoletti, Roberto A remark on almost complex quantization in symplectic fibrations, Indagationes Mathematicae, Volume 12 (2001) no. 2, p. 243 | DOI:10.1016/s0019-3577(01)80029-x
  • Paoletti, Roberto Symplectic submanifolds in special position, Israel Journal of Mathematics, Volume 123 (2001) no. 1, p. 241 | DOI:10.1007/bf02784129

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