The monodromy conjecture for ideals

Let $\mathcal I=(f_1,\ldots,f_r)$ be an ideal in $\mathbb C[x_0,\ldots,x_n]$ whose associated subscheme $Y=V(\mathcal I)$ in $\mathbb C^{n+1}$ contains the origin. Let $\sigma:X'\rightarrow\mathbb C^{n+1}$ be the blow-up of $\mathbb C^{n+1}$ with center $Y$. For a small ball $B\subset\mathbb C^{n+1}$ around the origin, Monodromy conjecture. If $\mathbb L^{-s_0}$ is a pole of the local motivic Igusa zeta function associated with $\mathcal I$, then $e^{2\pi i s_0}$ is a zero or pole of the monodromy zeta function of $\mathcal I$ at a point in $\sigma^{-1}(B\cap Y)$. This conjecture predicts a correspondence between poles of motivic Igusa zeta functions and monodromy eigenvalues, generalizing the classical monodromy conjecture from principal ideals to arbitrary ideals. The paper investigates this question for a space monomial curve arising as the special fiber of an equisingular family whose generic fiber is a plane branch.