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 $H_I^{d+1}(R)$.