In deformation theory, CMCohen-Macaulay in codimension 2 is the first to be considered in higher order deformation. Does CMCohen-Macaulay in codim. 2 have some good property to work with? Does it somehow measure how singular a scheme is?
I am reading Hartshorne's deformation theory, and iI have difficulty to "see" why CCohen-MMacaulay in codim. 2 is a good object to work with.
Thank you very much