Let $n \geq 1$ be an integer, let $X = \mathbb{CP}^n$, and let $T X$ denote the holomorphic tangent bundle of $X$, viewed as a rank-$n$ complex vector bundle. Let $\mathcal O_X(1)$ be the hyperplane line bundle on $X$, and let
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\begin{align*}
H := c_1(\mathcal O_X(1)) \in H^2_{\mathrm{dR}}(X;\mathbb C)
\end{align*}
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be the hyperplane class, normalized by the condition that its restriction to a projective line satisfies
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\begin{align*}
\int_{\mathbb{CP}^1} H = 1.
\end{align*}
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Under the standard de Rham [cohomology ring](/theorems/2271) presentation
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\begin{align*}
H^*_{\mathrm{dR}}(X;\mathbb C) \cong \mathbb C[H]/(H^{n+1}),
\end{align*}