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

Abstract

a b s t r a c tLet I be a complete M-primary ideal in a two-dimensional regular local ring (R, M) with an algebraically closed residue field. Let v 1 , . . ., v n denote the Rees valuations of I. In the theory of degree functions Rees and Sharp have associated with I positive integers d(I, v 1 ), . . ., d(I, v n ) 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.