Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with complex-geometry
Search options not deleted
user 4790
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.
5
votes
Accepted
Determine complex analytic germ along a smooth compact curve via normal bundle?
This is equivalent to asking whether for any smooth curve $C$ on a complex manifold $X$, there is an analytic neighborhood of $C$ in $X$ that is equivalent to a neighborhood of $C$ in the normal bundl …
- 27k
2
votes
Generalizing the square theorem
There are many examples. Take $X := \mathbb A^1$ and $Y := \mathbb A^2 \smallsetminus \{(0,0)\}$; since all vector bundles on $X$ and $Y$ are trivial, it is sufficient to give an example of a vector b …
- 27k
10
votes
Accepted
Branched covers of compact Riemann surfaces
From your group-theoretic description, it seems to me that you are asking for a covering $S' \to S$ which is only ramified over one point of $S$, and the ramification index of each point of the invers …
- 27k
2
votes
Accepted
Rational functions on reduced complex varieties that extend to global holomorphic functions
Let $A$ be a noetherian integral domain, $K$ its field of fractions, and $f \in K$. Assume that for each maximal ideal $\frak m$ of $A$ the element $f \in K \subseteq K\otimes_{A}\hat{A}_{\frak m}$ is …
- 27k
5
votes
Accepted
Automorphism group of ruled surface
Any automorphisms of $X$ lies over an automorphism of $C$. It seems to me that there is a unique section $C \to X$ with trivial normal bundle, so this section should be carried to itself by an automor …
- 27k
5
votes
Accepted
When are the Smooth Sections of a Bundle Generated as a Module (over Smooth Functions) by th...
Swan has proved that taking global section gives an anti-equivalence between finitely generate projective $\Gamma^{\infty}(M)$-modules and $C^{\infty}$ vector bundles on $M$; this correspondence is fu …
- 27k
6
votes
Is there an obvious way for showing singularities are quotient?
This is essentially Abhyankar's lemma.
What VA says is correct. However, one can simply remark that the subgroups $(d\mathbb Z)^n$ for $d>0$ form a cofinal system of subgroups of finite index, and t …
- 27k
3
votes
sections of morphisms of complex spaces
I meant to write this as a comment, but it won't fit.
In my opinion, you are confusing the étale analytic with the étale algebraic topology. The étale analytic topology is essentially the same the sa …
- 27k
5
votes
Accepted
Uniformity of injectivity for maps associated to linear systems
I think this is true.
The condition implies that for some $n$ the sections of $L^{\otimes n}$ are base point free, so $L^{\otimes n}$ is obtained by pulling back $\mathcal O(1)$ along a map $X \to \m …
- 27k
14
votes
Accepted
Pushing Complex Structure Forward
For 1): take a double covering $E\to B$, where $E$ and $B$ are compact oriented surface of genus 3 and 2 respectively, and give $E$ a structure of Riemann surface with trivial automorphism group.
Abo …
- 27k
5
votes
Does a generic curve inside the space of curves with a node at a specific point have only fi...
Yes, a generic curve with one node at a fixed point of $\mathbb P^2$ over a field of characteristic $0$ has only that singularity. This is true in any degree $d$ at least $2$. By looking at a generic …
- 27k
12
votes
A simple question about the degree of some vector bundle over rational curve.
Complex curves with anti-holomorphic involutions correspond to real algebraic curves. Your involution has no fixed points, so your curve corresponds to a real curve $C$ of genus 0 with no real points …
- 27k
4
votes
What is the local structure of a general Artin stack?
The stack of curves of genus 0 with at most one node is a quotient stack (see The integral Chow ring of the stack of at most 1-nodal rational curves, but Edidin and Fulghesu), so you are fine in this …
- 27k