Canonical modules and Cohen-Macaulay linkage in a local ring Original Research Article

We show that for a codimension 2 unmixed ideal B whose canonical module has finite projective dimension, it is possible to link B to an ideal A by a Cohen-Macaulay ideal I so that either the depth of the canonical module of R/A is one more than the depth of the canonical module of R/B, or R/A is Cohen-Macaulay. Moreover, both the linking ideal I and the linked ideal A can be described in terms of certain submatrices of the maps in a finite free resolution of the canonical module of R/B.