The map $M\setminus\{0\}\to\mathbb{C}^{3}_{z_{0},z_{1},z_{2}}\setminus\{0\}$ is a biholomorphism. The $T^{2}$-action on the holomorphic functions is identified as

$$e^{i\theta_{1}}\cdot(z_{0},z_{1},z_{2})=(e^{-i\theta_{1}}z_{0},e^{i\theta_{1}}z_{1},z_{2}),\quad e^{i\theta_{2}}\cdot(z_{0},z_{1},z_{2})=(e^{-i\theta_{2}}z_{0},z_{1},e^{i\theta_{2}}z_{2}).$$

The holomorphic volume form $\Omega=-dz_{0}\wedge dz_{1}\wedge dz_{2}.$ Henceforth we identify $M$ with $\mathbb{C}^{3}$.