Indices of normalization of ideals

Abstract

We derive numerical estimates controlling the intertwined properties of the normalization of an ideal and of the computational complexity of general processes for its construction. In [8], this goal was carried out for equimultiple ideals via the examination of Hilbert functions. Here we add to this picture, in an important case, how certain Hilbert functions provide a description of the locations of the generators of the normalization of ideals of dimension zero. We also present a rare instance of normalization of a class of homogeneous ideals by a single colon operation.