Symplectic subvarieties of projective fibrations over symplectic manifolds
Paoletti, Roberto
Annales de l'Institut Fourier, Tome 49 (1999), p. 1661-1672 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

@article{AIF_1999__49_5_1661_0,
     author = {Paoletti, Roberto},
     title = {Symplectic subvarieties of projective fibrations over symplectic manifolds},
     journal = {Annales de l'Institut Fourier},
     volume = {49},
     year = {1999},
     pages = {1661-1672},
     doi = {10.5802/aif.1733},
     mrnumber = {2000h:53110},
     zbl = {0955.53018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1999__49_5_1661_0}
}

Paoletti, Roberto. Symplectic subvarieties of projective fibrations over symplectic manifolds. Annales de l'Institut Fourier, Tome 49 (1999) pp. 1661-1672. doi : 10.5802/aif.1733. http://gdmltest.u-ga.fr/item/AIF_1999__49_5_1661_0/

[A] D. Auroux, Asymptotically Holomorphic Families of Symplectic Submanifolds, GAFA, 7 (1997), 29-58. | MR 99b:57069 | Zbl 0912.53020

[D] S. Donaldson, Symplectic Submanifolds and Almost Complex Geometry, J. of Diff. Geom., 44 (1996), 666-705. | MR 98h:53045 | Zbl 0883.53032

[GLS] V. Guillemin, E. Lerman, S. Sternberg, Symplectic Fibrations and Multiplicity Diagrams, Cambridge University Press, 1996. | MR 98d:58074 | Zbl 0870.58023

[GS] V. Guillemin, S. Sternberg, Symplectic Techniques in Physics, Cambridge University Press, 1984. | MR 86f:58054 | Zbl 0576.58012

[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 86d:14013 | Zbl 0547.14009

[MS] D. Mcduff, D. Salamon, Introduction to Symplectic Topology, Clarendon Press, Oxford, 1995. | MR 97b:58062 | Zbl 0844.58029

[M] D. Mumford, J. Fogarty, F. Kirwan, Geometric Invariant Theory, Springer Verlag, 1994. | MR 95m:14012 | Zbl 0797.14004

[S] A. Sommese, Submanifolds of Abelian Varieties, Math. Ann., 233 (1978), 229-256. | MR 57 #6524 | Zbl 0381.14007

[W] A. Weinstein, A Universal Phase Space for Particles in a Yang-Mills Field, Lett. Math. Phys., 2 (1977), 417-420. | MR 80e:58023 | Zbl 0388.58010