A Singularity Theorem for Twistor Spinors
  We study spin structures on orbifolds. In particular, we show that if the singular set has codimension greater than 2, an orbifold is spin if and only if its smooth part is. On compact orbifolds, we show that any non-trivial twistor spinor admits at most one zero which is singular unless the orbifold is conformally equivalent to a round sphere. We show the sharpness of our results through examples. 
Florin Belgun, Nicolas Ginoux, Hans-Bert Rademacher