On the Equations De.ning 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 AT] of height n. Suppose I/I ² is free AT]/I-module of rank n and (AT]/I) is torsion in K ₀(AT]). It is proved in this article that I is a set theoretic complete intersection ideal in AT] 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.