ScalingStacks

Likewise in the star type region case, up to $C^{\infty}$ small error in the $s^{-1}\log z^{m_{i}}$ coordinates,

$$\begin{cases}\omega_{CY,s}\approx\frac{1}{4}\frac{\partial^{2}u_{\infty,m}}{\partial x^{m_{i}}\partial x^{m_{j}}}\sqrt{-1}s^{-1}d\log z^{m_{i}}\wedge s^{-1}d\overline{\log z^{m_{j}}},\\ g_{CY,s}\approx\text{Re}\{\frac{1}{2}\frac{\partial^{2}u_{\infty,m}}{\partial x^{m_{i}}\partial x^{m_{j}}}s^{-1}d\log z^{m_{i}}\otimes s^{-1}d\overline{\log z^{m_{j}}}\}.\end{cases}$$

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