Lower bounds on heights of odd degree points of hyperelliptic curves
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918089110585344 |
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| author | Laga, Jef Thorne, Jack A. |
| author_facet | Laga, Jef Thorne, Jack A. |
| contents | We develop a reduction theory for the representation of $\mathrm{SL}_n$ on pairs of symmetric $n\times n$ matrices. We apply this theory to the pencils of quadrics arising from divisors on hyperelliptic curves. We use these results to show that, in a density $1$ family, an odd degree point $P$ of degree at most $2g-1$ on the hyperelliptic curve $z^2 = f_0x^{2g+2} + f_1 x^{2g+1} y + \cdots + f_{2g+2}y^{2g+2}$ cannot have small Weil height. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08652 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lower bounds on heights of odd degree points of hyperelliptic curves Laga, Jef Thorne, Jack A. Number Theory Algebraic Geometry We develop a reduction theory for the representation of $\mathrm{SL}_n$ on pairs of symmetric $n\times n$ matrices. We apply this theory to the pencils of quadrics arising from divisors on hyperelliptic curves. We use these results to show that, in a density $1$ family, an odd degree point $P$ of degree at most $2g-1$ on the hyperelliptic curve $z^2 = f_0x^{2g+2} + f_1 x^{2g+1} y + \cdots + f_{2g+2}y^{2g+2}$ cannot have small Weil height. |
| title | Lower bounds on heights of odd degree points of hyperelliptic curves |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2507.08652 |