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Immersed spheres in symplectic 4-manifolds. (English) Zbl 0756.53021

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.
Reviewer: D.McDuff

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
53C40 Global submanifolds
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References:

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