I am not very familiar with this material. Do you mind giving me some extra details? Specifically I would like to know what the $\Gamma$ are, why $\Gamma$ is the $\pi_1$ of a punctured nbhd of the singular point and why for punctured nbhds of toric surface singularities $\pi$ must be abelian (I realised this list is everything you said unfortunately :( ). I realise I'm asking a lot, I'd be grateful if you could point me to some references for those facts if you don't want to type up the details. Thank you for your help! EDIT: I can probably find a list of the $\Gamma$ on my own actually.