Curves with stable or semistable normal bundle on Fano hypersurfaces
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866916715385847808 |
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| author | Ran, Ziv |
| author_facet | Ran, Ziv |
| contents | For every $n\geq 3, g\geq 1$ and all large enough $e$ depending on $n,g$, there exist curves of genus $g$, degree $e$ in a general hypersurface of degree $n$ in $\mathbb P^n$, or in $\mathbb P^n$ itself, whose whose normal bundle $N$ is stable, as is any sufficiently general full-rank subsheaf of $N$. For $g=1$, $N$ is semi-stable. On general hypersurface of degree $d< n$ in $\mathbb P^n$, such that a certain arithmetical condition on $d,n, g $ holds, there exists an arithmetical progression of $e$ values so that curves of degree $e$ and genus $g$ with semistable normal bundle exist. Previous results were restricted to certain cases with ambient space $¶^n$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_12661 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Curves with stable or semistable normal bundle on Fano hypersurfaces Ran, Ziv Algebraic Geometry 14n25, 14j45, 14m22 For every $n\geq 3, g\geq 1$ and all large enough $e$ depending on $n,g$, there exist curves of genus $g$, degree $e$ in a general hypersurface of degree $n$ in $\mathbb P^n$, or in $\mathbb P^n$ itself, whose whose normal bundle $N$ is stable, as is any sufficiently general full-rank subsheaf of $N$. For $g=1$, $N$ is semi-stable. On general hypersurface of degree $d< n$ in $\mathbb P^n$, such that a certain arithmetical condition on $d,n, g $ holds, there exists an arithmetical progression of $e$ values so that curves of degree $e$ and genus $g$ with semistable normal bundle exist. Previous results were restricted to certain cases with ambient space $¶^n$ |
| title | Curves with stable or semistable normal bundle on Fano hypersurfaces |
| topic | Algebraic Geometry 14n25, 14j45, 14m22 |
| url | https://arxiv.org/abs/2211.12661 |