Saturations of powers of certain determinantal ideals

Abstract

Let $R$ be a Noetherian local ring and $m$ a positive integer. Let $I$ be the ideal of $R$ generated by the maximal minors of an $m\times (m+1)$ matrix $M$ with entries in $R$. Assuming that the grade of the ideal generated by the $k$-minors of $M$ is at least $m-k+2$ for $1\le \forall k\le m$, we will study the associated primes of $I^n$ for $\forall n>0$. Moreover, we compute the saturation of $I^n$ for $1\le \forall n\le m$ in the case where $R$ is a Cohen-Macaulay ring and the entries of $M$ are powers of elements that form an sop for $R$.

Cited by in corpus (1)

• *-transforms of acyclic complexes