Example 15.23.96C568E91A192

Example 15.23.9.6C568E91A192 If $n=2$ and $Z$ is a point on a compact Kähler surface, $[\theta ]=\pi ^*[h]+c[E]$ has Zariski positive part $\pi ^*[h]$ and negative part $cE$: $E^2=-1$ and $\pi ^*[h]\cdot E=0$. Its volume is $\int _ Yh^2$, although it is non-nef. The solution with $\kappa =1$ for the measure $\pi ^*(h^2)$ has logarithmic coefficient exactly $c$, its density vanishes to order $|z|^2$ along $E$, and the completion of its metric on $X\setminus E$ collapses $E$ to the point $Z$. The stronger barrier from proposition 15.23.2 has coefficient $c+\delta $.