Bass Numbers of the First Nonzero Local Cohomology Module

Abstract

Let $R$ be a regular local ring containing a field, let $I$ be an ideal with $d=\text{ht}{I}$, and assume $\text{ht}{p}=d$ for every minimal prime $p$ of $I$. We compute the Bass numbers $\mu^{0}(q,H_{I}^{d}(R))$ and $\mu^{1}(q,H_{I}^{d}(R))$ for all primes $q$. We then study $\mu^{2}(q,H_{I}^{d}(R))$ by considering the associated primes of $H_{I}^{d+1}(R)$.