Linkage on arithmetically Cohen–Macaulay schemes with application to the classification of curves of maximal genus

In this paper we provide a generalization of classical linkage, i.e. linkage by a complete intersection of dimension 0 or 1 on arithmetically Cohen-Macaulay schemes of any dimension. We prove some results related to the invariance of the deficiency module under such linkage and we apply these results and techniques to the classification of curves C in of maximal genus.