(Negative vertex) By a similar argument, in the negative vertex setting (cf. Section 1.1.5) the curvature 2-form $F$ satisfies

(1.18)

$$-\frac{1}{2\pi}dF=-\frac{\sqrt{-1}}{4\pi}\left(\frac{\partial^{2}W^{p\bar{q}}}{\partial\mu\partial\mu}+4\frac{\partial^{2}V}{\partial\eta_{p}\partial\bar{\eta}_{q}}\right)d\mu\wedge d\eta_{p}\wedge d\bar{\eta}_{q}=S,$$

where $S=\{z_{1}+z_{2}=1\}=\{e^{2\pi i\eta_{1}}+e^{2\pi i\eta_{2}}=1\}\subset\mathbb{C}^{*}_{z_{1}}\times\mathbb{C}^{*}_{z_{2}}\times\{0\}\subset\mathbb{C}^{*}_{z_{1}}\times\mathbb{C}^{*}_{z_{2}}\times\mathbb{R}_{\mu}$ defines a codimension 3 cycle. Here $S$ is endowed with the complex orientation, and the orientation on $\mathbb{C}^{*}_{z_{2}}\times\mathbb{R}_{\mu}$ is defined by the form $d\mu\wedge d\text{Re}\eta_{1}\wedge d\text{Im}\eta_{1}\wedge d\text{Re}\eta_{2}\wedge d\text{Im}\eta_{2}$.