On the equations defining curves in a polynomial algebra

Let A be a commutative Noetherian ring of dimension n (n ≥ 3). Let I be a local complete intersection ideal in A[T ] of height n. Suppose I/I is free A[T ]/I-module of rank n and (A[T ]/I) is torsion inK0(A[T ]). It is proved in this paper that I is a set theoretic complete intersection ideal in A[T ] if one of the following conditions holds: (1) n ≥ 5, odd; (2) n is even, and A contains the field of rational numbers; (3) n = 3 , and A contains the field of rational numbers. MSC: Primary 13C10; Secondary 13C40