Definition 20.4.116EC6FB71DCF4

Definition 20.4.11.6EC6FB71DCF4 A Bott–Chern b-divisor class over $Y$ is a family

indexed by the smooth compact modifications of $Y$ and compatible with pushforward: $g_*\mathbb A_{Z'}=\mathbb A_ Z$ whenever $g:Z'\to Z$ is a modification over $Y$. It is pseudoeffective if every $\mathbb A_ Z$ is pseudoeffective. It is Cartier if there are a model $Z$ and a class $a_ Z\in H^{1,1}_{\mathrm{BC}}(Z,\mathbb R)$ such that $\mathbb A_{Z'}=g^*a_ Z$ for every model $g:Z'\to Z$ dominating $Z$; the pair $(Z,a_ Z)$ is then called a Cartier realization of $\mathbb A$.