Disentangling mappings defined on ICIS

Let $(X,S)$ be an isolated complete intersection singularity of dimension $n$, and let $f:(X,S)\to ({\mathbb{C}}^{n+1},0)$ be a germ of $\mathcal{A}$-finite mapping. In this master’s degree final project, our main contribution is that we show the case $n=2$ of the general Mond conjecture, which states that ${\mu }_I(X,f)\ge {\text{codim}}_{{\mathcal{A}}_e}(X,f)$, with equality provided $(X,f)$ is weighted homogeneous. Before this project, the only known case for which the conjecture was known to hold is in the case that $n=1$ and $(X,S)$ is a plane curve.