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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.15213 |
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| _version_ | 1866917970939215872 |
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| author | Manni, Riccardo Salvati Freitag, Eberhard |
| author_facet | Manni, Riccardo Salvati Freitag, Eberhard |
| contents | In [ Ge], Bert van Geemen computed the dimension of the space of the fourth power of the theta nullwerte.
In [SM2], it has been observe that all linear relations between the $θ_m^4$ are consequences of the quartic Riemann relations.
In this note, we want to give a new proof of these result and extend them.
In a last section we treat the linear dependencies between arbitrary powers $\vartheta[m]^k$. We will show that $k=4$ is the only case where such dependencies can occur.
For this reason, we give a slightly different title: Some remarks to a Theorem of van Geemen |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some remarks to a Theorem of van Geemen Manni, Riccardo Salvati Freitag, Eberhard Algebraic Geometry Number Theory In [ Ge], Bert van Geemen computed the dimension of the space of the fourth power of the theta nullwerte. In [SM2], it has been observe that all linear relations between the $θ_m^4$ are consequences of the quartic Riemann relations. In this note, we want to give a new proof of these result and extend them. In a last section we treat the linear dependencies between arbitrary powers $\vartheta[m]^k$. We will show that $k=4$ is the only case where such dependencies can occur. For this reason, we give a slightly different title: Some remarks to a Theorem of van Geemen |
| title | Some remarks to a Theorem of van Geemen |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2501.15213 |