Abstract
An even linkage class L of two-codimensional subschemes in P n has a natural partial ordering given by domination. In this paper we give a necessary condition for X ∈ L to be integral in terms of its location in the poset structure on L . The condition is almost sufficient in the sense that if a subscheme dominates an integral subscheme and satisfies the necessary conditions, then it can be deformed with constant cohomology to an integral subscheme. In particular, the necessary conditions are sufficient in the case that Lazarsfeld and Rao originally studied, since the minimal element for L was a smooth connected space curve.
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