Stability of normal bundles of Brill-Noether curves
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909404508454912 |
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| author | Coskun, Izzet Smith, Geoffrey |
| author_facet | Coskun, Izzet Smith, Geoffrey |
| contents | We prove that the normal bundle of a general Brill-Noether curve of genus $g \geq 1$ and degree $d$ in $\mathbb{P}^r$ is semistable if $g=1$ or $g\geq \left \lceil \frac{5r}{2}\right\rceil r(r-1)$, or $d$ is larger than an explicit function of $g$ and $r$. We further prove that the normal bundle is in fact stable if $g\geq 2$ and either $g$ or $d$ satisfy slightly stronger bounds. In particular, for each $r$ and $g\geq 1$ (respectively, $g\geq2$), there are at most finitely many $(d,g)$ for which the normal bundle of the general Brill-Noether curve is not semistable (respectively, stable). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_12653 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability of normal bundles of Brill-Noether curves Coskun, Izzet Smith, Geoffrey Algebraic Geometry 14H60 (Primary) 14B99 (Secondary) We prove that the normal bundle of a general Brill-Noether curve of genus $g \geq 1$ and degree $d$ in $\mathbb{P}^r$ is semistable if $g=1$ or $g\geq \left \lceil \frac{5r}{2}\right\rceil r(r-1)$, or $d$ is larger than an explicit function of $g$ and $r$. We further prove that the normal bundle is in fact stable if $g\geq 2$ and either $g$ or $d$ satisfy slightly stronger bounds. In particular, for each $r$ and $g\geq 1$ (respectively, $g\geq2$), there are at most finitely many $(d,g)$ for which the normal bundle of the general Brill-Noether curve is not semistable (respectively, stable). |
| title | Stability of normal bundles of Brill-Noether curves |
| topic | Algebraic Geometry 14H60 (Primary) 14B99 (Secondary) |
| url | https://arxiv.org/abs/2306.12653 |