Let $\psi$ be the $(1,1)$-current in Proposition 3.31, then the following holds:

1. (1)

   The cohomology class $[\partial_{z}\psi(z)]\in H^{2}(D;\mathbb{R})$ is given by $k_{-}[\omega_{D}]$ and $k_{+}[\omega_{D}]$ for $z<0$ and $z>0$ respectively.

2. (2)

   At $z=0$, we have

   (3.381)

   $$\partial_{z}\psi(0)=\frac{1}{2}(k_{-}+k_{+})\omega_{D}.$$

   In particular, it extends smoothly across $P$.