in this question https://mathoverflow.net/a/55528/61732 it is stated that a normal variety is CM outside a set of codim at least 3. That would imply that normal surfaces are CM. [edited:] I wanted to ask if under the assumption that the variety is CM, the canonical divisor being Cartier is equivalent to the local rings being Gorenstein.

I would love to have a good book or paper on these questions with focus on algebraic geometry, cause I did not find any.

Many thanks, Lukas