Absolute bounds on the number of generators of Cohen-Macaulay ideals of height two

Abstract

For a Noetherian local domain $A$, there exists an upper bound $N_\tau(A)$ on the minimal number of generators of any height two ideal $\mathfrak a$ for which $A/\mathfrak a$ is Cohen-Macaulay of type $\tau$. If $A$ contains an infinite field, then we may take $N_\tau(A):=(\tau+1)e_{\textup{hom}}(A)$, where $e_{\textup{hom}}(A)$ is the homological multiplicity of $A$.