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 $\dim_{\mathbb{C}} \mathcal{O}_n/\text{Jac}(f)$, where $\text{Jac}(f)$ denotes the ideal generated by the Jacobian of $f$.

If $f:(\mathbb{C}^n,0) \to (\mathbb{C}^p,0)$ is an analytic germ map with that is an isolated complete intersection singularity, then it is also possible to find a nice algebraic description for the Milnor number of $f$. (See for instance Proposition 5.12 of "E. J. N. Looijenga, Isolated singular points on complete intersections, London Math. Soc. Lecture Notes Series 77 (1984), Cambridge University Press.")

I was not able to find a definition for the Milnor number for an analytic germ map with isolated singularities. Hence my question is if is it possible to define such number, or any reference addressing the problem of such definition.

Thanks in advance.


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