Degeneracy of holomorphic mappings into or avoiding Fermat type hypersurfaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913441434828800 |
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| author | Huynh, Dinh Tuan |
| author_facet | Huynh, Dinh Tuan |
| contents | We prove that if $f\colon\mathbb{C}^p\rightarrow\mathbb{P}^n(\mathbb{C})$ is a holomorphic mapping of maximal rank whose image lies in the Fermat hypersurface of degree $d>(n+1)\max\{n-p,1\}$, then its image is contained in a linear subspace of dimension at most $\bigg[\dfrac{n-1}{2}\bigg]$. Analog in the logarithmic case is also given. Our result strengthens a classical result of Green and provides a Nevanlinna theoretic proof for a recent result due to Etesse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14907 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Degeneracy of holomorphic mappings into or avoiding Fermat type hypersurfaces Huynh, Dinh Tuan Complex Variables Algebraic Geometry We prove that if $f\colon\mathbb{C}^p\rightarrow\mathbb{P}^n(\mathbb{C})$ is a holomorphic mapping of maximal rank whose image lies in the Fermat hypersurface of degree $d>(n+1)\max\{n-p,1\}$, then its image is contained in a linear subspace of dimension at most $\bigg[\dfrac{n-1}{2}\bigg]$. Analog in the logarithmic case is also given. Our result strengthens a classical result of Green and provides a Nevanlinna theoretic proof for a recent result due to Etesse. |
| title | Degeneracy of holomorphic mappings into or avoiding Fermat type hypersurfaces |
| topic | Complex Variables Algebraic Geometry |
| url | https://arxiv.org/abs/2405.14907 |