Hilbert samuel polynomial and its coefficients

Abstract

The Hilbert Samuel function measures the length of quotients by powers of an m primary ideal in a local ring R with maximal ideal m Samuel showed that this function agrees with a polynomial called the Hilbert Samuel polynomial for large powers of ideals We study the coefficients of this polynomial called as Hilbert coefficients We investigate the Hilbert coefficients and their relation to the structural properties of the ring and various blow up algebras We obtain characterizations for th