= Symplectic ball chart in complex projective space
{title2=$w\mapsto[w:\sqrt{1-|w|^2}]$}
Normalize the <Fubini-Study form> so that a <complex projective line> has <symplectic area> $\pi$. The displayed map takes the unit <symplectic ball> in $\mathbb C^n$ diffeomorphically onto the complement of the last-coordinate hyperplane. Its lift to the unit sphere has last coordinate positive real, so that coordinate contributes zero to the pulled-back <standard symplectic form>. The map is therefore a <symplectomorphism>.
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