Immersed spheres in symplectic 4-manifolds

Dusa McDuff

Annales de l'institut Fourier (1992)

  • Volume: 42, Issue: 1-2, page 369-392
  • ISSN: 0373-0956

Abstract

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We discuss conditions under which a symplectic 4-manifold has a compatible Kähler structure. The theory of -holomorphic embedded spheres is extended to the immersed case. As a consequence, it is shown that a symplectic 4-manifold which has two different minimal reductions must be the blow-up of a rational or ruled surface.

How to cite

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McDuff, Dusa. "Immersed spheres in symplectic 4-manifolds." Annales de l'institut Fourier 42.1-2 (1992): 369-392. <http://eudml.org/doc/74958>.

@article{McDuff1992,
abstract = {We discuss conditions under which a symplectic 4-manifold has a compatible Kähler structure. The theory of $J$-holomorphic embedded spheres is extended to the immersed case. As a consequence, it is shown that a symplectic 4-manifold which has two different minimal reductions must be the blow-up of a rational or ruled surface.},
author = {McDuff, Dusa},
journal = {Annales de l'institut Fourier},
keywords = {Kähler surfaces; symplectic 4-manifold; Kähler structure; - holomorphic embedded spheres; blow-up},
language = {eng},
number = {1-2},
pages = {369-392},
publisher = {Association des Annales de l'Institut Fourier},
title = {Immersed spheres in symplectic 4-manifolds},
url = {http://eudml.org/doc/74958},
volume = {42},
year = {1992},
}

TY - JOUR
AU - McDuff, Dusa
TI - Immersed spheres in symplectic 4-manifolds
JO - Annales de l'institut Fourier
PY - 1992
PB - Association des Annales de l'Institut Fourier
VL - 42
IS - 1-2
SP - 369
EP - 392
AB - We discuss conditions under which a symplectic 4-manifold has a compatible Kähler structure. The theory of $J$-holomorphic embedded spheres is extended to the immersed case. As a consequence, it is shown that a symplectic 4-manifold which has two different minimal reductions must be the blow-up of a rational or ruled surface.
LA - eng
KW - Kähler surfaces; symplectic 4-manifold; Kähler structure; - holomorphic embedded spheres; blow-up
UR - http://eudml.org/doc/74958
ER -

References

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  14. [PW] T. PARKER and J. WOLFSON, A compactness theorem for Gromov's moduli space, preprint, 1991. 
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