Remark 3.1.7 . [04PJ]

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Remark 3.1.7.

It is well-known (see for instance [GHK15]) that $T_{\rho_{\mathscr{X}}}=\Id$ if and only the pair $(D,\Delta_{D}=\sum_{i=1}^{r}C_{i})$ is toric, or if and only if the charge $Q$ vanishes, where

Q=\chi_{\text{top}}(D\setminus\Delta_{D})=12+\sum_{i=1}^{r}(b_{i}-3).