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 answers only
not deleted
user 9871
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.
3
votes
Accepted
Semi-stability of $S^n\Omega_S$ with respect to $K_S$
Ciao Francesco!
The answer to your question is yes, and the work of Bogomolov you are looking for about semistability of the tangent space (for minimal surfaces of general type indeed, no need of ampl …
- 7,902
27
votes
Accepted
Is the complex structure of $\mathbb CP^n$ unique?
Let me write this too long comment as an answer.
As abx says, what we do know is
Theorem 1. If a Kähler manifold $X$ is homeomorphic to $\mathbb{CP}^n$, then $X$ is biholomorphic to it.
This is due to …
- 7,902
5
votes
Accepted
A big line bundle in complex compact manifold
At least in the projective setting the following holds true (this is taken from J. Kollár "Shafarevich maps and automorphic forms", Proposition 13.14.2).
Proposition. Let $X$ be a smooth projective va …
- 7,902
2
votes
Examples of surfaces with negative Kahler curvature operator
Examples of compact Kähler manifolds with non positive holomorphic bisectional curvature are given by:
Closed submanifolds of complex tori.
Smooth compact quotients of bounded symmetric domains.
M …
- 7,902
5
votes
Why Calabi-Yau manifolds should be complex?
I think that one possible answer is that a Calabi-Yau manifold is a Riemannian manifold $M$ with $SU(n)$ Riemannian holonomy, where $2n=\dim_\mathbb R M$.
Such a manifold is then necessarily complex, …
- 7,902
12
votes
Accepted
Homotopy type of a complex affine variety
If $X$ is smooth, and if you ask to have the same homotopy type of a CW complex of real dimension at most $n$, this is precisely the statement of the Andreotti-Frankel theorem.
It is true, more gener …
- 7,902
2
votes
Geometrical meaning of admissible hermitian metric on a line bundle
I don't know if this answers to your question, and very likely you already know it, but one easy fact is the following.
First of all an obvious necessary condition is that at the level of cohomology …
- 7,902
3
votes
Uniruled degenerations of abelian varieties
Maybe this can be of some help.
In this paper by K. Oguiso, you can find at the end an appendix by N. Nakayama. In this appendix he gives a theorem which describes the local structure of a degenerati …
- 7,902
0
votes
A question about nef classes on compact Kähler manifolds
Just for fun, here is an answer in the purely algebraic setting.
So, suppose that $X$ is irreducible projective algebraic of dimension $n$, $\alpha=c_1(\mathcal O_X(D))$ is the class of a nef diviso …
- 7,902
6
votes
Examples of Brody hyperbolic affine varieties which are not Kobayashi hyperbolic
Here is an answer to the second part of the first question. It has been communicated to me by Leandro Arosio.
The answer is: yes, there does exist a Stein manifold which is Brody hyperbolic but not K …
- 7,902
5
votes
Is hyperbolicity a Zariski open condition?
Kobayashi hyperbolicity (or Brody hyperbolicity, the two notions coincide for compact complex spaces), is an open condition with respect to the analytic topology. Thus, for instance, once you find an …
- 7,902
2
votes
What is the holomorphic sectional curvature?
Maybe you already were aware of that, or maybe it really doesn't answer to your question, but I'll try anyhow...
Take a look at this, Subsection 7.5 on page 39. The construction you talk about in you …
- 7,902
11
votes
Bott Chern cohomology via currents
When $X$ is a compact complex manifold, its Bott-Chern cohomology groups can be computed either by smooth forms or by currents. The proof of this fact can be found for instance in Demailly's book (lin …
- 7,902
11
votes
Why can we not always take a Kähler class to be in rational cohomology?
Since Artie Prendergast-Smith is not expanding his comment in an answer, let me do it. As I said in the comments, his comment is essentially THE answer to the OP question. But let me give some more de …
- 7,902
3
votes
Accepted
holomorphic sectional curvature and total scalar curvature
The answer to your question is exactly the same of the answer to this older question of mine. Enjoy!
- 7,902