Algebraic hyperbolicity of subvarieties of homogeneous varieties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912694087450624 |
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| author | Day, Andy B. Raha, Neelarnab |
| author_facet | Day, Andy B. Raha, Neelarnab |
| contents | We study the algebraic hyperbolicity of certain subvarieties of homogeneous varieties, building on the techniques introduced by Coskun-Riedl, Yeong and Mioranci. This generalizes earlier known results for hypersurfaces to higher codimensions. In particular, we observe that if $X=X_1\cap\cdots\cap X_k$ is a very general complete intersection of degree $d_j$ hypersurfaces $X_j$ in $\mathbb{P}^n$ with $k\leq n-2$, then $X$ is algebraically hyperbolic if $\sum d_j\ge 2n-k$, and $X$ is not algebraically hyperbolic if $\sum d_j\le 2n-k-2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic hyperbolicity of subvarieties of homogeneous varieties Day, Andy B. Raha, Neelarnab Algebraic Geometry Primary: 32Q45. Secondary: 14M17, 14M10 We study the algebraic hyperbolicity of certain subvarieties of homogeneous varieties, building on the techniques introduced by Coskun-Riedl, Yeong and Mioranci. This generalizes earlier known results for hypersurfaces to higher codimensions. In particular, we observe that if $X=X_1\cap\cdots\cap X_k$ is a very general complete intersection of degree $d_j$ hypersurfaces $X_j$ in $\mathbb{P}^n$ with $k\leq n-2$, then $X$ is algebraically hyperbolic if $\sum d_j\ge 2n-k$, and $X$ is not algebraically hyperbolic if $\sum d_j\le 2n-k-2$. |
| title | Algebraic hyperbolicity of subvarieties of homogeneous varieties |
| topic | Algebraic Geometry Primary: 32Q45. Secondary: 14M17, 14M10 |
| url | https://arxiv.org/abs/2511.05488 |