Symplectic equivalence of smooth projective hypersurfaces (source code)

= 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.