PomeExample 21.13.82.A14927C0973A Let us consider the example example 21.13.15 again, we consider the subvariety corresponding to $\sigma _7$. We have
\[ Q_{\sigma _7}=\Bigl \{ m\in P_ D: \langle m,(1,1) \rangle =0 \Bigr \} . \]
The situation is explained in 21.13.83.
F8805F2A5BD021.13.83 The face $Q_{\sigma _7}=\{ m\in P_ D:\langle m,(1,1)\rangle =0\} $ is the single point $\{ (0,0)\} $, of dimension $0$ rather than the expected $1$.We find that $\dim Q_{\sigma _7}=0$, but the expected dimension is $2-1=1$. So the corresponding divisor, namely the exceptional divisor on $\mathrm{Bl}_0\mathbb {P}^2$ is in the non-Kähler locus. Similarly, we can verify that the non-Kähler locus consists only of this divisor.
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