The classical *monodromy conjecture* was originally formulated by Igusa in the seventies and predicts a relation between two invariants of a polynomial, one originating from number theory and the other from differential topology. More precisely, it states that the poles of the motivic, or related, Igusa zeta function of a polynomial $f \in {\mathbb C}[x_0, \ldots, x_n]$ induce eigenvalues of the local monodromy action of $f$, seen as a function $f:{\mathbb C}^{n+1}\rightarrow {\mathbb C}$, on the cohomology of its Milnor fiber at some point $x \in f^{-1}(0) \subset {\mathbb C}^{n+1}$. Generalizing the motivic Igusa zeta function to an ideal and using the notion of Verdier monodromy, one can similarly formulate the monodromy conjecture for ideals. To date, both conjectures have only been proven in full generality for polynomials and ideals in two variables, see [@L] and [@VV], respectively. In higher dimension, various partial results were shown for one polynomial (see for instance the introduction of [@BV] for a list of references), but for multiple polynomials, the most general result so far is a proof for monomial ideals [@HMY].

In this article, the monodromy conjecture is investigated for a class of binomial ideals in arbitrary dimension that define space curves deforming 