On the degree function coefficients of complete ideals in two-dimensional regular local rings

Let I be a complete M-primary ideal in a two-dimensional regular local ring (R,M) with an algebraically closed residue field. Let v1, …, vn denote the Rees valuations of I. In the theory of degree functions Rees and Sharp have associated with I positive integers d(I,v1), …, d(I,vn) providing useful information about I. We have called these integers the degree function coefficients of I. Using Zariski’s theory of complete ideals in a two-dimensional regular local ring and recent work of Heinzer and Kim on complete ideals, we obtain new interpretations of the degree function coefficients of I. Some applications are given.