The tag has no wiki summary.

learn more… | top users | synonyms

7
votes
2answers
128 views

A question about the strict transform on blow-ups

I arrived at the following phrase at a material that I'm reading: Let $\pi :N'\rightarrow N$ be the blow-up of center $P$. For a given $a\in\mathcal{O}$ and $P'\in\pi^{-1}(P)$, the strict ...
2
votes
1answer
43 views

A question in germs and multiplicity of zeroes.

Suppose that I have $N$ a bidimensional analytical manifold, $\mathcal{F}$ a foliation in $N$, and let $P\in N$. Being $\mathcal{O}$ the local ring of germs of holomorphic functions in $P$, and ...
5
votes
1answer
74 views

Why are germs of functions important?

Why is it necessary to define germs of functions (in my case, for foliations, but my question is in general)? does any inconsistency arises if instead of using a germ in some context, I use ...
5
votes
1answer
94 views

germ finitely determined

Does anyone know any result on finitely determined germs to help me prove that the germ $f(x,y)=x^3+ xy^3$ is $4$- determined? I tried using the definition of germs finitely determined, which is:$f: ...
1
vote
0answers
64 views

Calculating germs for complete holomorphic function

I'm trying to find the germs $[z,f]$ for the complete holomorphic function $\sqrt{1+\sqrt{z}}$ . The question indicates that I should find 2 germs for z = 1, but I seem to be able to find 3! Where ...
2
votes
0answers
190 views

Nicer Description of Germs of Continuous Functions

I may be asking something a little out of my comfort zone at this moment so bear with me. Before I begin let me provide some background for the interested outsider: Let $X$ be a topological space ...