Bounds on the degree of two-codimensional integral varieties in projectivespace

In this paper we establish new upper bounds on the degree of a two-codimens ional nondegenerate 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 genera l hyperplane section of the variety which is not restriction of any element of the same degree in the defining ideal of the variety. (C) 2001 Elsevier Science B.V. All rights reserved.