12th Mini-Workshop on Singularities, Geometry and Differential Equations and 1st M...
Invariant manifolds and limit periodic sets of discontinuous foliations
| Full text | |
| Author(s): |
Calvo-Andrade, O.
;
Correa, M.
;
Fernandez-Perez, A.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | INTERNATIONAL JOURNAL OF MATHEMATICS; v. 28, n. 3 MAR 2017. |
| Web of Science Citations: | 0 |
| Abstract | |
We consider holomorphic foliations of dimension k > 1 and codimension >= 1 in the projective space P-n, with a compact connected component of the Kupka set. We prove that if the transversal type is linear with positive integer eigenvalues, then the foliation consists of the fibers of a rational fibration Phi : P-n -> Pn- k. As a corollary, if dim(F) >= cod(F) + 2 and has a transversal type diagonal with different eigenvalues, then the Kupka component K is a complete intersection and the leaves of the foliation define a rational fibration. The same conclusion holds if the Kupka set has a radial transversal type. Finally, as an application, we find a normal form for non-integrable codimensionone distributions on P-n. (AU) | |
| FAPESP's process: | 14/23594-6 - Holomorphic foliations with locally free tangent sheaf |
| Grantee: | Marcos Benevenuto Jardim |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |