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 1345
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
Continuous point map for spherical domains
Here’s an attempt to define such a map which is not an answer but couldn’t fit in a comment.
Consider a Riemann mapping $\varphi:\mathbb{H}^2 \to \overset{\circ}{D}$ (which has a continuous extension …
- 68.9k
9
votes
Complexifications of hyperbolic manifolds
There exist hyperbolic 3-manifolds which cannot embed totally geodesically in complex hyperbolic manifolds, answering this
question in the negative.
Recently it was shown that complex hyperbolic manif …
- 68.9k
12
votes
Accepted
Symplectic structure on the square of a 3-manifold
Let $M$ be a 3-manifold fibering over $S^1$, so there exists a fibration $\Sigma \to M \to S^1$.
Then $M\times M$ will admit a symplectic structure.
There is a symplectic structure on $M\times S^1$, a …
- 68.9k
31
votes
Accepted
Complex projective manifolds are homeomorphic if homotopy equivalent
For curves this follows from the classification of (2-dimensional topological) surfaces, and for simply-connected surfaces this follows from Freedman's theorem.
My former colleagues Anatoly Libgober a …
- 68.9k
6
votes
Accepted
On limits of manifolds
In general, this will be false. Examples are found among solenoidal manifolds, defined by Sullivan. For example, 1-dimensional solenoids.
Many of these are obtained by taking the inverse limit of fi …
- 68.9k
3
votes
Lattices of PU(n,1) with large abelianization
The other answers give fine examples, but I found a reference to the 1981 thesis of Livné which constructs complex hyperbolic lattice which admits a surjective holomorphic map to a Riemann surface. Th …
- 68.9k
2
votes
When is $\mathrm{Aut}(X)\times \mathrm{Aut}(Y)$ of finite index in $\mathrm{Aut}(X\times Y)$?
If $X$ or $Y$ is $\mathbb{D}^n$ (the unit complex ball) or $\mathcal{T}^n$ (Teichmuller space), then $Aut(X\times Y)$ will be finite index in $Aut(X)\times Aut(Y)$. This follows by considering the Kob …
CommunityBot
- 1
6
votes
Are non-isomorphic covers of riemann surfaces also generally nonisomorphic as riemann surfaces?
There's a remarkable theorem of Margulis that pertains to your question. Let $G$ be a semisimple Lie group (in your case, $PSL_2(\mathbb{R})$), and let $\Gamma$ be an irreducible lattice in $G$. The c …
- 47.3k
5
votes
Surface of a Ideal Tetrahedron in Hyperbolic Space H3
The surface of the tetrahedron is a 4-punctured sphere, made of 4 ideal triangles. In fact, this is a complete hyperbolic metric, as may be seen by sending $z_1$ to $\infty$ (in fact, we may assume $z …
- 68.9k
3
votes
Injective maps on cohomology and Kahler manifolds
Suppose one has compact symplectic manifolds $(X,\omega), (Y,\sigma)$, and a map $f:X\to Y$ such that $f^\ast\sigma=\omega$ (if $f$ is also a diffeomorphism, then this map is a symplectomorphism, but …
- 68.9k
12
votes
Accepted
A four-dimensional counterexample?
This paper by Hillmann addresses this question. He proves that a surface bundle over a surface which is a complex surface has a holomorphic fibration over the base, for some choice of complex structur …
- 68.9k
6
votes
Kähler structure on cotangent bundle?
In a paper by Goldman, Kapovich, and Leeb, it is pointed out that a fuchsian (surface) group embedded into the isometries of complex hyperbolic space has quotient the tangent bundle to the surface. Si …
- 68.9k
6
votes
Schwarz Lemma in terms of conformal surfaces or holomorphic curves?
I think the short answer to your question is no, since the notion of a holomorphic map is purely local, whereas the existence of a hyperbolic metric (uniformization) depends on the global structure of …
- 68.9k
5
votes
Rational Hilbert modular surfaces
I don't know the answer to this question, but here's a possible strategy to prove finiteness, following the approach of Zograf, as extended by Long and Reid for congruence arithmetic fuchsian groups o …
- 68.9k
36
votes
What do Weierstrass points look like?
I think another interpretation is in terms of Euclidean geometry instead of hyperbolic geometry. If $\omega$ is a holomorphic 1-form on a Riemann surface $\Sigma$, then $|\omega|$ defines a Euclidean …
- 68.9k