ScalingStacks

We choose a nonempty $E_{J}$ which realizes the maximum in (2.2), with $m=|J|-1$, and relabel so that $J=\{0,\dots,m\}$. We also denote by $U$ an open neighborhood of $E_{J}$ in $\mathfrak{X}$ which can be covered by finitely many adapted coordinate charts as above. In particular, in these charts we have

(3.1)

$$i^{n^{2}}\Omega_{t}\wedge\overline{\Omega_{t}}=|f_{J}|^{2}\prod_{j=1}^{m}i\frac{dz_{j}}{z_{j}}\wedge\frac{d\overline{z_{j}}}{\overline{z_{j}}}\wedge\prod_{k=m+1}^{n}idz_{k}\wedge d\overline{z_{k}}.$$