Riemann surface foliations with non-discrete singular set
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912284073263104 |
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| author | Gehlawat, Sahil |
| author_facet | Gehlawat, Sahil |
| contents | Let $\mathcal{F}$ be a singular Riemann surface foliation on a complex manifold $M$, such that the singular set $E \subset M$ is non-discrete. We study the behavior of the foliation near the singular set $E$, particularly focusing on singular points that admit invariant submanifolds (locally) passing through them. Our primary focus is on the singular points that are removable singularities for some proper subfoliation. We classify singular points based on the dimension of their invariant submanifold and, consequently, establish that for hyperbolic foliations $\mathcal{F}$, the presence of such singularities ensures the continuity of the leafwise Poincaré metric on $M \setminus E$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15920 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Riemann surface foliations with non-discrete singular set Gehlawat, Sahil Complex Variables 32S65, 32M25 (Primary) 30F45 (Secondary) Let $\mathcal{F}$ be a singular Riemann surface foliation on a complex manifold $M$, such that the singular set $E \subset M$ is non-discrete. We study the behavior of the foliation near the singular set $E$, particularly focusing on singular points that admit invariant submanifolds (locally) passing through them. Our primary focus is on the singular points that are removable singularities for some proper subfoliation. We classify singular points based on the dimension of their invariant submanifold and, consequently, establish that for hyperbolic foliations $\mathcal{F}$, the presence of such singularities ensures the continuity of the leafwise Poincaré metric on $M \setminus E$. |
| title | Riemann surface foliations with non-discrete singular set |
| topic | Complex Variables 32S65, 32M25 (Primary) 30F45 (Secondary) |
| url | https://arxiv.org/abs/2503.15920 |