Integral subschemes of codimension two Original Research Article

An even linkage class image of two-codimensional subschemes in image has a natural partial ordering given by domination. In this paper we give a necessary condition for image to be integral in terms of its location in the poset structure on image. 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 image was a smooth connected space curve.