Linkage by Generically Gorenstein, Cohen–Macaulay Ideals

In this paper, we study linkage by a wider class of ideals than the complete intersections. We are most interested in how the Cohen–Macaulay property behaves along this more general notion of linkage. In particular, if idealsAandBare linked by a generically Gorenstein Cohen–Macaulay idealI, and ifAis a Cohen–Macaulay ideal, we give a criterion forBto be a Cohen–Macaulay ideal. WhenR/Bis not Cohen–Macaulay, we can give in many cases an easy description of the non–Cohen–Macaulay locus ofR/B, and also a criterion forR/Bto have almost maximal depth.