Reconstruction of curves from their theta hyperplanes in genera $6$ and $7$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916729939034112 |
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| author | Çelik, Türkü Özlüm Lehavi, David |
| author_facet | Çelik, Türkü Özlüm Lehavi, David |
| contents | We derive a formula for reconstructing a generic complex canonical curve $C$ of genus 6 and 7 in terms of the theta hyperplanes of $C$. Hence, we get a generic inverse to the Torelli map, as well as a complete description of the Schottky locus in these genera. The computational part of the proof relies on a certified numerical argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02235 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reconstruction of curves from their theta hyperplanes in genera $6$ and $7$ Çelik, Türkü Özlüm Lehavi, David Algebraic Geometry Primary: 14H40, 14H42, 65G40, Secondary: 14H45, 14Q05, 14-04 We derive a formula for reconstructing a generic complex canonical curve $C$ of genus 6 and 7 in terms of the theta hyperplanes of $C$. Hence, we get a generic inverse to the Torelli map, as well as a complete description of the Schottky locus in these genera. The computational part of the proof relies on a certified numerical argument. |
| title | Reconstruction of curves from their theta hyperplanes in genera $6$ and $7$ |
| topic | Algebraic Geometry Primary: 14H40, 14H42, 65G40, Secondary: 14H45, 14Q05, 14-04 |
| url | https://arxiv.org/abs/2401.02235 |