Immersed spheres in symplectic 4-manifolds
Annales de l'Institut Fourier, Tome 42 (1992) no. 1-2, p. 369-392
Nous étudions des conditions sous lesquelles une variété symplectique de dimension 4 admet une structure kählérienne compatible. La théorie des sphères plongées J-holomorphes est généralisée au cas immergé. Nous démontrons comme conséquence qu’une variété symplectique de dimension 4 qui a deux réductions minimales, est nécessairement l’éclatement d’une surface rationnelle ou réglée.
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.
@article{AIF_1992__42_1-2_369_0,
     author = {Duff, Dusa Mc},
     title = {Immersed spheres in symplectic 4-manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {42},
     number = {1-2},
     year = {1992},
     pages = {369-392},
     doi = {10.5802/aif.1296},
     zbl = {0756.53021},
     mrnumber = {93k:53030},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1992__42_1-2_369_0}
}
Duff, Dusa Mc. Immersed spheres in symplectic 4-manifolds. Annales de l'Institut Fourier, Tome 42 (1992) no. 1-2, pp. 369-392. doi : 10.5802/aif.1296. http://www.numdam.org/item/AIF_1992__42_1-2_369_0/

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