(complex structure) The map $M^{+}\to\{\tilde{Z}_{0}\tilde{Z}_{1}\tilde{Z}_{2}=1-Z_{3}\}$ is a holomorphic open embedding. The $T^{2}$-action is identified as

$$e^{i\theta_{1}}\cdot(\tilde{Z}_{0},\tilde{Z}_{1},\tilde{Z}_{2})=(e^{-i\theta_{1}}\tilde{Z}_{0},e^{i\theta_{1}}\tilde{Z}_{1},\tilde{Z}_{2}),\quad e^{i\theta_{2}}\cdot(\tilde{Z}_{0},\tilde{Z}_{1},\tilde{Z}_{2})=(e^{-i\theta_{2}}\tilde{Z}_{0},\tilde{Z}_{1},e^{i\theta_{2}}\tilde{Z}_{2}),$$

and the holomorphic volume form is $\Omega=-\frac{\sqrt{-1}}{2\pi Z_{3}}d\tilde{Z}_{0}\wedge d\tilde{Z}_{1}\wedge d\tilde{Z}_{2}$. We shall identify $M^{+}$ with its image.