I guess it depends on what groups you are quotienting out by (finite groups, reductive groups?), anyway, for example see

• The cone of curves on algebraic varieties by Y. Kawamata, Prop. 1.7 and the following discussion in the finite group case.

For some generalities to non-finite groups, see

• Pure subrings of regular rings are pseudo-rational by Hans Schoutens, Theorem B

I guess it depends on what groups you are quotienting out by (finite groups, reductive groups?), anyway, for example see

• The cone of curves on algebraic varieties by Y. Kawamata, Prop. 1.7 and the following discussion in the finite group case.

For some generalities to non-finite groups, see

• Pure subrings of regular rings are pseudo-rational by Hans Schoutens, Theorem B

You can find some discussion I'm sure in other standard sources such as Flips and Abundance for Algebraic Threefolds by Koll'ar et. al. Also see Kollar-Mori.