  As was recently pointed out by McMullen and Taubes [Math. Res. Lett. 6 (1999)
681-696], there are 4-manifolds for which the diffeomorphism group does not act
transitively on the deformation classes of orientation-compatible symplectic
structures. This note points out some other 4-manifolds with this property
which arise as the orientation-reversed versions of certain complex surfaces
constructed by Kodaira [J. Analyse Math. 19 (1967) 207-215]. While this
construction is arguably simpler than that of McMullen and Taubes, its
simplicity comes at a price: the examples exhibited herein all have large
fundamental groups.
