Definition 20.1.10908967DFB37E

Definition 20.1.10.908967DFB37E A Cartier b-divisor $\mathbb {D}$ over $X$ is a Weil b-divisor $\mathbb {D}$ over $X$ such that there exists a modification $\pi \colon Y\rightarrow X$ and a class $\alpha _ Y\in \mathrm{H}^{1,1}(Y,\mathbb {R})$ so that for each $\pi '\colon Z\rightarrow X$ dominating $\pi $, the class $\mathbb {D}_ Z$ is the pull-back of $\alpha _ Y$. Any such $(\pi ,\alpha _ Y)$ is called a realization of $\mathbb {D}$.