Homogeneous pre-foliations of co-degree one and degree four on the projective plane
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909026999074816 |
|---|---|
| author | Pracias, Carla Luza, Maycol Falla |
| author_facet | Pracias, Carla Luza, Maycol Falla |
| contents | We classify, up to projective automorphism, all homogeneous pre-foliations of co-degree one and degree four on the complex projective plane $\Ptwo$ whose Legendre transform defines a flat $4$-web. The classification is organized according to the type of the underlying homogeneous foliation $\Hcal$ of degree~$3$, distinguishing the cases $°(\Tcal_{\Hcal})=2$, $3$, and~$4$. The case $°(\Tcal_{\Hcal})=2$ was treated by Bedrouni, while the cases $°(\Tcal_{\Hcal})=3$ and $°(\Tcal_{\Hcal})=4$ are completed here. The proof combines Bedrouni's curvature-holomorphy criteria with explicit normal forms and symbolic computation; the result yields a finite list of explicit one-forms, parametrised by the ramification data of the Gauss map of~$\Hcal$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07944 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homogeneous pre-foliations of co-degree one and degree four on the projective plane Pracias, Carla Luza, Maycol Falla Algebraic Geometry Complex Variables Dynamical Systems We classify, up to projective automorphism, all homogeneous pre-foliations of co-degree one and degree four on the complex projective plane $\Ptwo$ whose Legendre transform defines a flat $4$-web. The classification is organized according to the type of the underlying homogeneous foliation $\Hcal$ of degree~$3$, distinguishing the cases $°(\Tcal_{\Hcal})=2$, $3$, and~$4$. The case $°(\Tcal_{\Hcal})=2$ was treated by Bedrouni, while the cases $°(\Tcal_{\Hcal})=3$ and $°(\Tcal_{\Hcal})=4$ are completed here. The proof combines Bedrouni's curvature-holomorphy criteria with explicit normal forms and symbolic computation; the result yields a finite list of explicit one-forms, parametrised by the ramification data of the Gauss map of~$\Hcal$. |
| title | Homogeneous pre-foliations of co-degree one and degree four on the projective plane |
| topic | Algebraic Geometry Complex Variables Dynamical Systems |
| url | https://arxiv.org/abs/2605.07944 |