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 foliations
Search options not deleted
user 605
3
votes
7
votes
Accepted
Deformation of foliation
The same argument applies to codimension one foliations on compact $3$-folds with finite fundamental group. …
- 8,828
4
votes
An extra condition on Frobenius theorem for $1$-forms
The existence of a global closed $\alpha$ imposes strong restrictions on the foliation. The foliation would transversely affine, in the sense that there would exist an open covering of the ambient man …
- 8,828
6
votes
Accepted
Algebraicity and non-algebraicity of leaves of the characteristic foliation
If $A_1$ itself is a product of elliptic curves (or isogeneous to the product of an elliptic curve and an abelian variety of dimension $n-1$) then $A_1$ carries linear foliations with all leaves algebraic …
- 8,828
7
votes
Accepted
Holomorphic Foliations having transverse sections
The main references here are McQuillan's paper Canonical models of foliations; and Brunella's book Birational geometry of foliations.
Examples. … In contrast, it is rather easy to produce examples of foliations tranverse to curves of negative self-intersection. …
- 8,828
2
votes
Accepted
Extension of integrable distribution over a subset
The answer in general is no.
If $K$ is a submanifold of $M$ then tangent bundle of $K$ defines an integrable distribution on $K$. To wit we are talking about the foliation with just one leaf: $K$.
…
- 8,828
4
votes
Density of non-algebraic leaves in the characteristic foliation
For a foliation on a projective manifold $Y$, the set of points belonging to invariant subschemes with a given Hilbert polynomial is a Zariski closed subset of $Y$. Therefore the set of algebraic leav …
- 8,828
6
votes
Accepted
algebraic leaves of foliation on a product of two curves
The foliation $\mathcal F$ defined by $p_1^* \omega_1 + p_2^* \omega_2$ is everywhere transverse to the fibration $p_2 : S \to C$. One can therefore lift paths
from $C$ to leaves of $\mathcal F$ in …
- 8,828
4
votes
Accepted
Vector fields tangent to distributions with zero first Chern class
Not in general.
Let $F \in H^0(\mathbb P^3, \mathcal O_{\mathbb P^3}(3))$ be a general cubic form and let $H \in H^0(\mathbb P^3, \mathcal O_{\mathbb P^3}(1))$ be a linear form. The kernel of
$\omega …
- 8,828
7
votes
Accepted
Smooth rank one foliations with closed leaves
The problem makes sense for foliations of arbitrary dimensions. No need to be restricted to foliation by curves. … There are also examples of holomorphic foliations having all its leaves compact but with non-Hausdorff leaf-space, on non-compact complex manifolds, see On the stability of holomorphic foliations by Holmann …
- 8,828
13
votes
Accepted
References for holomorphic foliations
Brunella - Birational geometry of foliations
Suwa - Indices of vector fields and residues of holomorphic foliations
Gomez-Mont, Bobadilla - Sistemas Dinamicos Holomorfos en Superficies ( in Spanish ) … Touzet recently studied foliations admitting a transversal Kähler metric in this paper. …
- 8,828
6
votes
Foliations by holomorphic curves on complex surfaces
The same result holds true for codimension one foliations by compact leaaves, but it is not true for higher codimension foliations. …
- 8,828
3
votes
Existence transverse sections in $\mathbb{CP}^1$-bundles over compact Riemann surfaces
Therefore, in the particular case of foliations everywhere transverse to the fibration you are asking for the possible monodromy representations of projective structures on it. …
- 8,828
2
votes
Looking for examples of non-singular holomorphic foliations with compact leaves
The result is due to Edwards, Millett and Sullivan and appears in the paper Foliations with all leaves compact published by Topology. …
- 8,828