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Michael Albanese
Michael Albanese
12:38 AM
@MartinSleziak: Thanks for your reply.
 
 
5 hours later…
Martin Sleziak
Martin Sleziak
5:51 AM
specific-question What would be a suitable tag for this (bountied) question: Milnor Number of real and imaginary parts of holomorphic germs?
2
Q: Milnor Number of real and imaginary parts of holomorphic germs?

MarraBy 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...

singularity-theory several-complex-variables
 
 
6 hours later…
Martin Sleziak
Martin Sleziak
11:26 AM
On MathOverflow it is generally recommended to use at least one top-level tag, see: Why are MO tags formatted as they are? and Frequently asked questions about tagging on MathOverflow. I am not familiar with the topic, so I should leave the choice of tags to the OP and to more experienced users. (I considered (ag.algebraic-geometry) and (cv.complex-variables), but maybe there are more suitable choices of tags. — Martin Sleziak 2 mins ago
Is the tag milnor-invariant suitable for questions about Milnor number? (There are some questions tagged in such way.)
2
Q: Bounds for the milnor number of a hypersurface singularity

eventuallyI 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!

singularity-theory ag.algebraic-geometry milnor-invariant
4
Q: On the milnor number of analytic germ map

User43029If $f:(\mathbb{C}^n,0) \to (\mathbb{C},0)$ 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...

ac.commutative-algebra complex-geometry singularity-theory milnor-invariant
Milnor number
In mathematics, and particularly singularity theory, the Milnor number, named after John Milnor, is an invariant of a function germ. If f is a complex-valued holomorphic function germ then the Milnor number of f, denoted μ(f), is either a nonnegative integer, or is infinite. It can be considered both a geometric invariant and an algebraic invariant. This is why it plays an important role in algebraic geometry and singularity theory. == Geometric interpretation == Consider a holomorphic complex function germ f: f : ( C...
Link group
In knot theory, an area of mathematics, the link group of a link is an analog of the knot group of a knot. They were described by John Milnor in his Bachelor's thesis, (Milnor 1954). == Definition == The link group of an n-component link is essentially the set of (n + 1)-component links extending this link, up to link homotopy. In other words, each component of the extended link is allowed to move through regular homotopy (homotopy through immersions), knotting or unknotting itself, but is not allowed to move through other component. This is a weaker condition than isotopy: for example,...
 

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