All Questions
Tagged with analytic-geometry cv.complex-variables
9
questions
37
votes
2
answers
2k
views
Residues in several complex variables
I am trying to educate myself about the basics of the theory of residues in several complex variables. As is usually written in the introduction in the textbooks on the topic, the situation is much ...
- 1,180
31
votes
3
answers
4k
views
Complex analytic vs algebraic geometry
This is more of a philosophical or historical question, and I can be totally wrong in what I am about to write next.
It looks to me, that complex-analytic geometry has lost its relative positions ...
- 1,180
7
votes
0
answers
155
views
Finite covers in complex analytic geometry
Given a complex manifold or complex analytic space, one has the standard notion of open set. There are two different Grothendieck topologies that one can define using this notion, one where covers ...
- 1,168
3
votes
1
answer
317
views
Is a compact subset of a Stein space admitting a fundamental system of Stein neighbourhoods necessarily holomorphically convex?
Let X be a Stein manifold and let K be a compact subset of X. Suppose that K possesses in X a fundamental system of neighbourhoods which are Stein spaces. Then, it is a result by Rossi that such a ...
- 169
2
votes
2
answers
1k
views
Conformal mappings that preserve angles and areas but not perimeters?
Conformal mappings from $U$ to $V$, both subsets of $\mathbb{C}$, locally preserve angles.
But, in general, such mappings neither preserve areas nor preserve perimeters.
Q. Are there examples of ...
- 149k
2
votes
1
answer
343
views
Is the closure of an open holomorphically convex subset of a Stein space holomorphically convex?
Let X be a Stein manifold and U an open, connected, relatively compact, holomorphically convex subset of X. Is the closure of U in X holomorphically convex?
Also, if X is a Stein space with a finite ...
- 169
2
votes
0
answers
58
views
Differentiable functions on analytic varieties
Let $\iota\colon X\to \Omega\subseteq \mathbb{C}^n$ be a complex analytic variety $X$ in an open subset $\Omega$ of $\mathbb{C}^n$. If $N$ is a smooth manifold and $h\colon M\to X$ is a continuous map,...
- 393
1
vote
1
answer
128
views
Bounded holomorphic functions on hypersurfaces of $\Bbb C^n$
Is it true that every bounded holomorphic functions on a smooth analytic hypersurface $X$ of $\Bbb C^n$ is constant?
Remark that if $X$ is algebraic, the answer is yes.
Otherwise can you provide ...
- 13
-3
votes
1
answer
200
views
Conformal map from a 7-sided polyhedron to a square pyramid
I have a right-angled square pyramid, $A$, whose height and base-length are $l$. By 'right-angled', I mean that the apex of $A$ lies vertically above one of the vertices in its base. Now supposed I ...
- 167