S. K. Donaldson, ‘Symplectic submanifolds and almost-complex geometry’Symplectic submanifolds and almost-complex geometry, J. Differential Geom. Volume 4444, Number 4666 (1996).
For more info, 666–705and the link to Bertini's theorem, see Jonathan Evans' thesis: Symplectic topology of some Stein and rational surfaces.