Integral subschemes of codimension two

An even linkage class L of two-codimensional subschemes in P-n has a natura l partial ordering given by domination. In this paper we give a necessary c ondition for X is an element of L to be integral in terms of its location i n the poset structure on L. The condition is almost sufficient in the sense that if a subscheme dominates an integral subscheme and satisfies the nece ssary conditions, then it can be deformed with constant cohomology to an in tegral subscheme. In particular, the necessary conditions are sufficient in the case that Lazarsfeld and Rao originally studied, since the minimal ele ment for L was a smooth connected space curve. (C) 1999 Elsevier Science B. V. All rights reserved.