Lemma 2.1 . [0227]

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Lemma 2.1.

As long as the NA MA equation holds

\det(D^{2}u)(\sum\frac{\partial u}{\partial x_{i}}d_{i})^{n-m}=\text{const},

then the generalized Calabi ansatz $dd^{c}u$ is a Calabi-Yau metric, in this case of proportional line bundles.