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.
Nous étudions des conditions sous lesquelles une variété symplectique de dimension 4 admet une structure kählérienne compatible. La théorie des sphères plongées -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.
@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}, pages = {369--392}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {42}, number = {1-2}, year = {1992}, doi = {10.5802/aif.1296}, zbl = {0756.53021}, mrnumber = {93k:53030}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1296/} }
TY - JOUR AU - Duff, Dusa Mc TI - Immersed spheres in symplectic 4-manifolds JO - Annales de l'Institut Fourier PY - 1992 SP - 369 EP - 392 VL - 42 IS - 1-2 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1296/ DO - 10.5802/aif.1296 LA - en ID - AIF_1992__42_1-2_369_0 ER -
Duff, Dusa Mc. Immersed spheres in symplectic 4-manifolds. Annales de l'Institut Fourier, Volume 42 (1992) no. 1-2, pp. 369-392. doi : 10.5802/aif.1296. https://aif.centre-mersenne.org/articles/10.5802/aif.1296/
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