curve given by $$\label{eq:equations-Y}
        \left\{\begin{array}{r c l l}
        f_1:= x_1^{n_1} & - & x_0^{n_0}  &  = 0 \\
        f_2:= x_2^{n_2}  &- & x_0^{b_{20}}x_1^{b_{21}} &= 0  \\
        & \vdots & &\\
        f_g := x_g^{n_g} &- & x_0^{b_{g0}}x_1^{b_{g1}}\cdots x_{g-1}^{b_{g(g-1)}} & = 0.\\
        \end{array}\right.$$ This is still an irreducible curve which is smooth outside the origin. One can also show that the equations $f_1,\ldots, f_g$ form a regular sequence in ${\mathbb C}[x_0,\ldots, x_g]$; this can, for example, be done by showing that the map ${\mathbb C}[x_0,\ldots,x_i] \rightarrow {\mathbb C}[t^{{\bar{\beta}}_0},\ldots, t^{{\bar{\beta}}_i}]$ defined by $x_j \mapsto t^{{\bar{\beta}}_j}$ is a surjective ring homomorphism with kernel $(f_1,\ldots, f_i)$, which implies the even stronger property that every $(f_1,\ldots,f_i)$ is a prime ideal in ${\mathbb C}[x_0,\ldots,x_g]$. Finally, as such a monomial curve for $g = 1$ is just a cusp in the complex plane, of which the monodromy conjecture is well-known, we will assume that $g \geq 2$.

The monodromy conjecture for ideals {#MonodromyGeneral}
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This section provides a short introduction to the monodromy conjecture for ideals, focusing on the motivic version. Let ${\mathcal I}= (f_1, \ldots, f_r)$ be a non-trivial ideal in ${\mathbb C}[x_0, \ldots, x_n]$ and let $Y := V({\mathcal I})$ be its associated subscheme in the 