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Denote by $R = \mathbb{C}\{x_1, \dots, x_n\}$ the ring of germs of analytics maps at the origin in $n$ variables and let $f \in R$ such that $Sing(V(f))=V(x_1, \dots, x_{n-1})$ as sets. In addition, ...

Let $R = \mathbb{C}\{x_1, \dots,x_n\}$ be the ring of germs of analytic functions and let $f \in R$ be a homogeneus polynomial of degree $p$ such that $\sqrt{Jac(f)}=\langle x_1, \dots, x_{n-1}\rangle ...

If $f:(\mathbb{C}^n,0) \to (\mathbb{C},0)$ is an analytic germ with an isolated singularity, then the Milnor number of $f$, denoted by $\mu(f)$ can be defined as $\dim_{\mathbb{C}} \mathcal{O}_n/\text{...