Degenerate Second Main Theorems for Holomorphic Curves in Different Geometric Settings
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910199605886976 |
|---|---|
| author | Quang, Si Duc Van An, Nguyen Hai, Tran An |
| author_facet | Quang, Si Duc Van An, Nguyen Hai, Tran An |
| contents | We establish second main theorems for holomorphic curves into a projective subvary $V \subset \mathbb{P}^n(\mathbb{C})$ of dimension $k$, intersecting hypersurfaces in $N$-subgeneral position with respect to $V$ $(N > k)$. Our results provide explicit truncation levels for the counting functions that are independent of the number of hypersurfaces. The theorems are obtained in several settings, including holomorphic curves on $\mathbb{C}$, annuli, complex discs with finite growth index, and Kähler manifolds. We obtain a total defect bound that improves upon the previously known results. As an application, we establish a corresponding form of Schmidt's subspace theorem for families of homogeneous polynomials in subgeneral position. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02371 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Degenerate Second Main Theorems for Holomorphic Curves in Different Geometric Settings Quang, Si Duc Van An, Nguyen Hai, Tran An Complex Variables We establish second main theorems for holomorphic curves into a projective subvary $V \subset \mathbb{P}^n(\mathbb{C})$ of dimension $k$, intersecting hypersurfaces in $N$-subgeneral position with respect to $V$ $(N > k)$. Our results provide explicit truncation levels for the counting functions that are independent of the number of hypersurfaces. The theorems are obtained in several settings, including holomorphic curves on $\mathbb{C}$, annuli, complex discs with finite growth index, and Kähler manifolds. We obtain a total defect bound that improves upon the previously known results. As an application, we establish a corresponding form of Schmidt's subspace theorem for families of homogeneous polynomials in subgeneral position. |
| title | Degenerate Second Main Theorems for Holomorphic Curves in Different Geometric Settings |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2406.02371 |