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Results tagged with complex-geometry
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user 21522
Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
6
votes
1
answer
2k
views
Puiseux series expansion for space curves?
This result is apparently well known and used by many people.
I am, however, quite frustrated that I cannot seem to find a proof that I can understand.
For plane algebraic curves, this is not too hard …
- 1,111
8
votes
0
answers
934
views
Etymology of the O-notation for algebras of holomorphic functions
The notation $O(X)$ seems to be a quite standard notation for the algebra of all holomorphic functions on some connected domain in $\mathbb{C}^n$ (or a complex manifold). I would like to know where di …
- 1,111
3
votes
0
answers
407
views
Connections between the "local parametrization theorem" and "Noether normalization theorem"
In the study of local theory for holomorphic varieties, the Local Parametrization Theorem states that in $\mathbb{C}^n$,for any irreducible germ of holomorphic variety $V$ at 0, there exist a nonsingu …
- 1,111
4
votes
1
answer
520
views
Weighted projective space with rational or real weights
The most common formulation of the weighted projective space is perhaps the global quotient
$$
(\mathbb{C}^{n+1} \setminus \{(0,\ldots,0\}) / \mathbb{C}^\ast
$$
with the $\mathbb{C}^\ast$ group action …
- 1,111
2
votes
1
answer
716
views
How to study the nonregular part of a finite branched holomorphic covering?
A finite branched holomorphic covering is a holomorphic map $f : V \to W$
between holomorphic varieties $V$ and $W$ such that
$f$ is a finite branched covering (in the topological sense)
There is a …
- 1,111