In this article we find upper bounds on the Rao function for space curves i
n terms of the degree, genus and the minimal degree s of a surface which co
ntains the curve. These bounds are shown to be sharp for s less than or equ
al to 4. This paper is dedicated to David Buchsbaum on the occasion of his
70th birthday. (C) 2000 Elsevier Science B.V. All rights reserved.