is $$\label{eq:rel-gcd-lcm}
    \gcd\Big(\frac{m}{m_1}, \ldots, \frac{m}{m_r} \Big) = \frac{m}{\operatorname{lcm}(m_1,\ldots, m_r)}.$$ Finally, by a *complex variety*, we mean a reduced separated scheme of finite type over ${\mathbb C}$, which is not necessarily irreducible. A *curve* is a variety of dimension one, and a *surface* a variety of dimension two.

**Acknowledgement.** The authors would like to thank Hussein Mourtada for the idea of investigating the monodromy conjecture for the class of space monomial curves with a plane semigroup. The first author would also like to thank the Fulbright Program (within the José Castillejo grant by Ministerio de Educación, Cultura y Deporte) for its financial support while writing this paper and the University of Illinois at Chicago, especially Lawrence Ein, for the warm welcome and support in hosting him.

Space monomial curves with a plane semigroup {#SpaceMonomial}
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We start this article with introducing the class of monomial curves we are interested in. They arise in a natural way as the special fibers of equisingular families of curves whose generic fibers are isomorphic to some plane branch. More precisely, let ${{\mathcal C}:= {\{f = 0\}} \subset ({\mathbb C}^2,0)}$ be the germ at the origin of an irreducible plane curve defined by a complex irreducible 