 Symplectic equivalence of smooth projective hypersurfaces

Any two smooth degree-$d$ hypersurfaces in ${\mathbb{CP}}^n$, equipped with the restricted Fubini-Study form, are symplectomorphic. Join them through the connected complement of the discriminant in the parameter space, use the resulting smooth family to identify the fibers, and apply Moser's trick to the cohomologous restricted forms.