but as it turns out (I think it's a result by Arnol'd but don't quote me on that), if you know an implicit equation that generates the hypersurface, you can simply compute the R-codimension of the implicit equation!

the thing about the Milnor number is that, when you have a hypersurface with isolated singularities, it can be retracted into a bouquet (a wedge of k-spheres) around those singularities

the number of spheres is called the milnor number, and the canonical way to compute it is, well, compute the homology :⁾

seems like every time you have something in the form (x,y²,something of order ≥ 2) the Tjurina number is 3, regardless

Me: there is no way students don't get confused with this shit

Students: [get confused with that shit and think Df is a function]

Me: figures

@ZevenKorian Perhaps it has something to do with the rotational symmetry of Minkowski space?

I thought "well maybe it's because if you have a local isometry--" but the minkowski space is not isometric to the sphere?

I just cheated and looked it up on wikipedia (don't do this at home kids!) and it seems like they coincide on the minkowski space, on S², on...

- Pronouns
- She · Her

- Languages
- 🇪🇸 🇬🇧 CAT

- Main account
- @Sheepy

- Interests
- Singularity theory, topology, complex analysis

Please bear in mind this is graduate-level maths most of the time. It's okay if it goes over your head, this level of math is super niche and abstract anyway.

Site map:

Public account: @Koishi

Math account: @ZevenKorian (you're here)

Main account: @Sheepy

Private account: @Luchtspieg

Joined Oct 2018