Hamiltonian reduction for unit sphere

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Let $(M, \omega)$, be Symplectic Vector space and $N\subset M$ be unit sphere. Then why $N/ker\omega\mid _N$ is naturally $\mathbb{P}^{n-1}(\mathbb{C})$

Here ker$\omega$=$\{ y\in M: \omega(x,y)=0, \forall x\in M\}$