Generic $\mathcal{A}$-finite determinacy and singularities of homogeneous polynomial mappings

We make a detailed investigation of the generic properties that polynomial mappings possess. An important starting point is the work by Farnik, Jelonek and Ruas in 2019, where they prove some of those properties in the context of homogeneous polynomial mappings of $\mathbb{C}^3$ to $\mathbb{C}^3$, and conclude the genericity of $\mathcal{A}$-finite determinacy by applying the geometric criterion. Using their strategy, we further extend and generalize some of their key findings to dimensions greater than or equal to $2$, though some of those properties can only be extended up to dimension $4$.