Integrally normalized Fubini-Study form
= Integrally normalized Fubini-Study form
{title2=$[\omega_{\rm int}]=c_1(\mathcal O(1))$}
The form $\omega_{\rm int}=\frac{i}{2\pi}\partial\bar\partial\log(1+\sum|z_j|^2)$ patches on <Complex projective space>. The dual tautological metric on $\mathcal O(1)$ identifies it with normalized <Chern curvature>, so $[\omega_{\rm int}]=c_1(\mathcal O(1))$. With the unnormalized convention $i\partial\bar\partial\log(1+\sum|z_j|^2)$, divide by $2\pi$ to obtain this integral class.