Reference for orbifolds in string- and M-theory

Question

A number of orbifold constructions have been studied heavily in string- and M-theory over the years, establishing various dualities between different theories.

Can someone point me to a slightly more mathematical reference where the basics of orbifolds, and things like smoothening or blowing up are explained in a way that may be useful for string theory? Specifically, given, say $T^4/\mathbb{Z}_2$, what is a systematic way to analyze a particular theory on such an orbifold.

I know a few standard cases, like M-theory on $S^1/\mathbb{Z}_2$ is the strongly-coupled version of the $E_8 \times E_8$ heterotic string, and $K3$ is in an orbifold limit described by $T^4/\mathbb{Z}_2$. Of course the standard way seems to be to pick up various math results from papers by Aspinwall, Witten, etc. but I want to know something about a systematic understanding of orbifolds, computing fixed points in the fundamental domain, etc. in a way that seems eventually intuitive.

This post imported from StackExchange Physics at 2016-06-08 08:51 (UTC), posted by SE-user leastaction

Comments

math.colostate.edu/~renzo/teaching/Orbifolds/Ruan.pdf

This post imported from StackExchange Physics at 2016-06-08 08:51 (UTC), posted by SE-user Jake