Journal of Symplectic Geometry
Volume 10 (2012)
Symplectic generic complex structures on four-manifolds with $b_+ = 1$
Pages: 493 – 502
We study symplectic structures on Kähler surfaces with $p_g = 0$. We give an example of a projective surface which admits a symplectic structure which is not compatible with any Kähler metric.