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

In this paper the author provides a generalization of classical linkage, i.e. linkage by a complete intersection of dim. 0 or 1 on arithmetically Cohen-Macaulay schemes of any dimension. Namely she looks at residuals in the scheme theoretic intersection of an aCM scheme of dim. r (resp. r+1) with r hypersurfaces of degree a_1,...,a_r. When the aCM scheme is singular a complete intersection on it may not be Gorenstein, in this case classical linkage, even if suitably generalized, does not apply. The main purpose of this paper is to prove some results related to the invariance of the deficiency module under such linkage. In the last part of the paper the author shows how to apply these results and techniques to the classification of curves C in P^n of degree d and maximal genus G(d, n, s) among those not contained in surfaces of degree less than a certain fixed one s.