By performing some computations using the Singular software, I've noticed the following pattern: if $\mu$ is the Milnor Number of a holomorphic germ $f\in \mathcal{O}_n$ at the origin, then the Milnor Number of its real and imaginary parts are equal and are $\mu^2$, that is, $$ \mu_{(\mathcal{R}e...
I am having a hard time in finding an upper bound in terms of the degree and the dimension for the Milnor number of an isolated hypersurface singularity. I am mostly interested in surfaces on the projective space. Can some one please give me a hint on this? Thanks!
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:(\ma...
« first day (2342 days earlier) ← previous day next day → last day (1558 days later) »