Uloženo v:
| Hlavní autoři: | , |
|---|---|
| Médium: | Preprint |
| Vydáno: |
2025
|
| Témata: | |
| On-line přístup: | https://arxiv.org/abs/2505.16632 |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
Obsah:
- In this paper, we study homogeneous convex foliations on the complex projective plane $\mathbb{P}^2$. A foliation is called convex if all of its leaves, except straight lines, have no inflection points, and such foliations form a Zariski closed subset in the space of degree $d$ foliations on $\mathbb{P}^2$. Using projective duality, every foliation can be associated with a $d$-web on the dual plane via its Legendre transform, and it is known that the Legendre transform of a homogeneous convex foliation is flat. Our first main result provides a classification of homogeneous convex foliations admitting exactly three radial singularities on the line at infinity. As a second result, we complete the classification of convex homogeneous foliations of degree $6$, extending previous classifications in degrees $4$ and $5$.