Definition 5.20.149FE903B6E5A8

Definition 5.20.14.9FE903B6E5A8Assume that $L$ is a pseudo-effective line bundle on $X$. A Fubini–Study metric on $L$ is a psh metric $h$ on $L$ of the following form: There exists $m\in \mathbb {Z}_{>0}$, finitely many sections $s_1,\ldots ,s_ N\in \mathrm{H}^0(X,L^ m)$ and $\lambda _1,\ldots ,\lambda _ N\in \mathbb {Q}$ such that for any local nowhere vanishing holomorphic section $s$ of $L$, we have

We write $\mathrm{FS}(L)$ for the set of Fubini–Study metrics on $L$.