Bounds on the degree of two-codimensional integral varieties in projective space

In this paper we establish new upper bounds on the degree of a two-codimensional non-degenerate integral variety in projective space, depending on the dimension of the variety and on a non-lifting level s for it, i.e. a level such that there is an element of degree s in the defining ideal of a general hyperplane section of the variety which is not restriction of any element of the same degree in the defining ideal of the variety.