Hilbert functions, Castelnuovo-Mumford regularity and uniform Artin-Rees numbers (Q1382649)

The main result of this paper is that, for a finitely generated CM-module \(M\) over a local ring \((A,m)\), the Hilbert coefficients and postulation number of \(M\) are bounded in terms of the multiplicity and dimension of \(M\), with respect to an \(m\)-primary ideal. As application one gets a bound on the reduction number of \(m\)-primary ideals in rings of positive depth, in terms of the Hilbert coefficients of the ideal. Another application concerns uniform Artin-Rees number of a pair of modules \(M\subseteq N\), which is explicit if \(M/N\) is CM.