Talk:Milnor number

Untitled[edit]

1. What is Milnor's book on Morse theory here for? Was it a mistake? (I've added his complex hypersurfaces book)

2. There ought to be something about vanishing homology and the Milnor fibre

Simplifix (talk) 18:15, 8 November 2008 (UTC)[reply]

You're quite right: there should be something about the vanishing cycles on the Milnor fibre. Please feel free to add something. Δεκλαν Δαφισ (talk) 18:16, 9 November 2008 (UTC)[reply]

3. The examples section is a little too informal, I quote: "two is a nice number". —Preceding unsigned comment added by 137.222.10.58 (talk) 15:04, 28 September 2010 (UTC)[reply]

4. The conventions here are inconsistent: defining $\mathcal{O}$ as the ring of function germs $(\mathbb{C}^n, 0) \rightarrow (\mathbb{C}, 0)$ means that all functions in $\mathcal{O}$ must vanish at $0$ (i.e. we're defining $\mathcal{O} = \mathfrak{m} \mathcal{O_{\mathbb{C}^n, 0}}$, the maximal ideal of the local coordinate ring of $\mathbb{C}^n$). This means that the examples are incorrect: in example $1$, a function $h(x,y) = k + x h_1(x,y) + y h_2(x,y)$ is only in $\mathcal{O}$ when $k = 0$, so by the definition above, $\mu$ would be $0$. Similarly, $\mu$ would not even be well-defined in the case of a non-singular point. — Preceding unsigned comment added by 140.180.240.149 (talk) 19:56, 10 June 2015 (UTC)[reply]

This article needs more clean up[edit]

I did what I could. I think further changes should be made with a new set of eyes. The article is formal enough, but lacks some formatting and cleaning up, eg Reference section, I don't have a clue how to fix it. Paczki sa nalepsze z dzemem (talk) 22:38, 16 April 2021 (UTC)[reply]