Saturations of powers of certain determinantal ideals

Abstract

In this paper we study certain determinantal ideals that extend the class of ideals of Herzog-Northcott type introduced by O'Carroll and Planas-Vilanova. As is well known, in a three-dimensional Cohen-Macaulay local ring, the second symbolic powers of ideals of Herzog-Northcott type can be controlled well. We aim to generalize this fact considering ``saturation" instead of ``symbolic power." Furthermore, in order to compare the saturation with the symbolic power, we study the associated primes of the powers of certain determinantal ideals.