Let $X=\mathbb{P}^{n}_{\mathbb{C}}$ and $L={\mathcal{O}}(1)$, the universal line bundle of $\mathbb{P}^{n}_{\mathbb{C}}$. A rational section $s$ of ${\mathcal{O}}(1)$ can be identified with a homogeneous rational function $\rho_{s}\in\mathbb{C}(x_{0},\dots,x_{n})$ of degree 1. The poles of this section coincide which those of $\rho_{s}$. For a point $p=(p_{0}:\dots:p_{n})\in\mathbb{P}^{n}(\mathbb{C})$ outside this set of poles, the Fubini-Study metric of ${\mathcal{O}}(1)^{{\text{\rm an}}}$ is defined as

$$\|s(p)\|_{\operatorname{FS}}=\frac{|\rho_{s}(p_{0},\dots,p_{n})|}{(\sum_{i}|p_{i}|^{2})^{1/2}}.$$

Clearly, this definition does not depend on the choice of a representative of $p$. The pair $({\mathcal{O}}(1),\|\cdot\|_{{\operatorname{FS}}})$ is a metrized line bundle.