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 5259
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
2
answers
333
views
Fixed-point free holomorphic involutions
Here is the new version of the question which is more explicit. The older version is below.
I am looking for complex projective varieties (in dimensions $2$ and higher) admitting a fixed-point free ho …
4
votes
0
answers
148
views
Looking for some abelian surface fibration
Do you know of any explicit smooth complex projective threefold $X$ with an Abelian surface fibration over $\mathbb{P}^1$ such that $K_X = [-F]$ where $F$ is the fiber class divisor.
I am not lookin …
2
votes
1
answer
331
views
almost holomorphic line bundles
Let $(L,\omega_L) \to (M,\omega_M)$ be a symplectic line bundle (symplectic line=real dimension 2) over a symplectic manifold $M$. Each of these objects can be equipped with an almost complex structur …
3
votes
1
answer
256
views
Local holomorphic equations for symplectic divisors
If $(X,\omega)$ is a symplectic manifold and $J\colon TX \to TX$ is an almost complex structure, we know that $J$ is actually a complex structure if and only if the Nijenhuis tensor $N_J(\cdot,\cdot)$ …
3
votes
1
answer
602
views
top chern class
Let $E\to M$ be a holomorphic vector bundle ($M$ is compact) and assume $s\colon M\to E$ is a non-trivial section transverse to the zero section.
Is it be possible that $s^{-1}(0)\neq \emptyset$, ye …
3
votes
2
answers
606
views
Deforming to decompose vector bundles
After edit:
How do we show that for every (holomorphic) vector bundle over a curve, is it possible to deform it to another one which is decomposable (into line bundles)?
Before edit:
I am not sure …
1
vote
1
answer
329
views
$P^1$ minus k points
For $k\geq 3$, and $k$ arbitrary points $S=( z_1,\cdots,z_k ) \in \mathbb{P}^1$, we can write
$$ P^1 \setminus S \cong \mathbb{H}/G $$
where $\mathbb{H}$ is the upper-half plane and $G\subset PSL(2 …
2
votes
2
answers
2k
views
Toroidal embedding
Its known ( see " The birational geometry of degenerations") that there exist a smooth one parameter family (i.e. total space is smooth) of two dimensional complex toris over unit disk whose central f …
2
votes
Kähler structure on cotangent bundle?
In the reference mentioned by Zemisch, Guillemin and Stenzel prove:
Theorem. For an analytic manifold $L$ and analytic metric $g$ on $L$,
there is a $\sigma$-invariant neighborhood ($\sigma(x,v)=(x,-v …
5
votes
1
answer
638
views
A simple question about the degree of some vector bundle over rational curve.
Let $E$ be a holomorphic vector bundle (infact complex vector bundle is enough) over $\mathbb{P}^1$. Let $c: \mathbb{P^1} \rightarrow \mathbb{P^1}$ be the anti-holomorphic involution, $c(z)=\frac{-1} …
0
votes
Cone of movable curves
I think following post in the mathoverflow gives an answer:
Effective versus movable cones of curves
There, people mention that there is an example where the Ample cone is rational polyhedral but mo …
9
votes
3
answers
3k
views
Cone of movable curves
Let $X$ be a smooth complex projective variety of dimension $n$.
Under the duality between $N_1(X)$ and $N^1(X)$ we know that closure of cone of effective curves $\overline{NE}(X)$ is dual to closure …
16
votes
4
answers
3k
views
Moduli space of genus 2 curves
Does any body know any reference in which the geometry of compactified moduli space of genus two curves ( Which is a three dimensional variety/stack/...) has been studied?
2
votes
0
answers
636
views
canonical bundle of Abelian surface fibrations
For minimal surfaces admitting an elliptic fibration over a smooth curve,
there is a famous analysis of possible singular fibers and a canonical bundle formula due to Kodaira.
There are two papers of …
2
votes
0
answers
327
views
surfaces with effective first Chern class
Let $S$ be a smooth complex surface, If $c_1(S) \in N_1(S)$ is nef and non-torsion, then we know that this would imply some restrictions on the cone of effective curves (and surface itself)--see the d …