\[MonodromyGeneral\], we discuss the monodromy conjecture for ideals in more detail, and in Section \[MonodromyWeighted\], we present the A’Campo formula for the zeta function of monodromy in terms of an embedded ${\mathbb Q}$-resolution. Section \[RedCurveSurface\] explains how the monodromy eigenvalues of a space monomial curve $Y \subset {\mathbb C}^{g+1}$ relate to those of $Y$ seen as a Cartier divisor on a generic embedding surface $S$. Then, we construct an embedded ${\mathbb Q}$-resolution of $Y$ on such a generic surface $S$ in Section \[Resolution\], and we use the A’Campo formula with this resolution to compute the monodromy zeta function in Section \[ZetaFunction\]. Finally, in Section \[MonConj\], we give a proof of the monodromy conjecture for this class of curves.

We end the introduction with fixing some notation used throughout this article. We let ${\mathbb N}$ be the set of non-negative integers. The greatest common divisor and lowest common multiple of a set of integers $m_1,\ldots,m_r \in \mathbb Z$ is denoted by $\gcd(m_1,\ldots, m_r)$ and $\operatorname{lcm}(m_1,\ldots,m_r)$, respectively. To shorten the notation, we will sometimes use $(m_1,\ldots, m_r)$ for the greatest common divisor. A useful relation between these two numbers for $m_1,\ldots, m_r$ a set of non-zero integers and $m$ a common multiple 