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| Main Author: | |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1904.08905 |
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| _version_ | 1866918279839219712 |
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| author | Shaska, Tanush |
| author_facet | Shaska, Tanush |
| contents | For a superelliptic curve $\mathcal X$, defined over $\mathbb Q$, let $\mathfrak p$ denote the corresponding moduli point in the weighted moduli space. We describe a method how to determine a minimal integral model of $\mathcal X$ such that: i) the corresponding moduli point $\mathfrak p$ has minimal weighted height, ii) the equation of the curve has minimal coefficients. Part i) is accomplished by reduction of the moduli point which is equivalent with obtaining a representation of the moduli point $\mathfrak p$ with minimal weighted height, as defined in [5], and part ii) by the classical reduction of the binary forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1904_08905 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Superelliptic curves with minimal weighted moduli height Shaska, Tanush Number Theory For a superelliptic curve $\mathcal X$, defined over $\mathbb Q$, let $\mathfrak p$ denote the corresponding moduli point in the weighted moduli space. We describe a method how to determine a minimal integral model of $\mathcal X$ such that: i) the corresponding moduli point $\mathfrak p$ has minimal weighted height, ii) the equation of the curve has minimal coefficients. Part i) is accomplished by reduction of the moduli point which is equivalent with obtaining a representation of the moduli point $\mathfrak p$ with minimal weighted height, as defined in [5], and part ii) by the classical reduction of the binary forms. |
| title | Superelliptic curves with minimal weighted moduli height |
| topic | Number Theory |
| url | https://arxiv.org/abs/1904.08905 |