Symplectic subvarieties of projective fibrations over symplectic manifolds

Roberto Paoletti

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 5, page 1661-1672
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Paoletti, Roberto. "Symplectic subvarieties of projective fibrations over symplectic manifolds." Annales de l'institut Fourier 49.5 (1999): 1661-1672. <http://eudml.org/doc/75397>.

@article{Paoletti1999,
abstract = {Given a symplectic fibration $E\rightarrow M$, 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.},
author = {Paoletti, Roberto},
journal = {Annales de l'institut Fourier},
keywords = {symplectic submanifold; projective fibration; almost complex structure; Poincaré dual; almost Hodge structure},
language = {eng},
number = {5},
pages = {1661-1672},
publisher = {Association des Annales de l'Institut Fourier},
title = {Symplectic subvarieties of projective fibrations over symplectic manifolds},
url = {http://eudml.org/doc/75397},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Paoletti, Roberto
TI - Symplectic subvarieties of projective fibrations over symplectic manifolds
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 5
SP - 1661
EP - 1672
AB - Given a symplectic fibration $E\rightarrow M$, 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.
LA - eng
KW - symplectic submanifold; projective fibration; almost complex structure; Poincaré dual; almost Hodge structure
UR - http://eudml.org/doc/75397
ER -

References

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  1. [A] D. AUROUX, Asymptotically Holomorphic Families of Symplectic Submanifolds, GAFA, 7 (1997), 29-58. Zbl0912.53020MR99b:57069
  2. [D] S. DONALDSON, Symplectic Submanifolds and Almost Complex Geometry, J. of Diff. Geom., 44 (1996), 666-705. Zbl0883.53032MR98h:53045
  3. [GLS] V. GUILLEMIN, E. LERMAN, S. STERNBERG, Symplectic Fibrations and Multiplicity Diagrams, Cambridge University Press, 1996. Zbl0870.58023MR98d:58074
  4. [GS] V. GUILLEMIN, S. STERNBERG, Symplectic Techniques in Physics, Cambridge University Press, 1984. Zbl0576.58012MR86f:58054
  5. [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. Zbl0547.14009MR86d:14013
  6. [MS] D. MCDUFF, D. SALAMON, Introduction to Symplectic Topology, Clarendon Press, Oxford, 1995. Zbl0844.58029MR97b:58062
  7. [M] D. MUMFORD, J. FOGARTY, F. KIRWAN, Geometric Invariant Theory, Springer Verlag, 1994. Zbl0797.14004MR95m:14012
  8. [S] A. SOMMESE, Submanifolds of Abelian Varieties, Math. Ann., 233 (1978), 229-256. Zbl0381.14007MR57 #6524
  9. [W] A. WEINSTEIN, A Universal Phase Space for Particles in a Yang-Mills Field, Lett. Math. Phys., 2 (1977), 417-420. Zbl0388.58010MR80e:58023

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