A Curve of Secants to the Kummer Variety from Degenerate Points
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913031920812032 |
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| author | Aburto, José Alejandro |
| author_facet | Aburto, José Alejandro |
| contents | We prove that, under certain geometric conditions, that only \(m-1\) different non-degenerate \((m+2)\)-secant \(m\)-planes plus one degenerate \((m+2)\)-secant \(m\)-plane to the Kummer variety implies the existence of a curve of ${(m+2)}$-secants to the Kummer variety. This is done by constructing a set of equations in terms of theta functions from the germ of a curve on the described points. The relation between those equations allows to proceed by induction to get the entire desired curve since the first of them is equivalent to the hypothesis that we ask. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12393 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Curve of Secants to the Kummer Variety from Degenerate Points Aburto, José Alejandro Algebraic Geometry 14K25, 14H40 (Primary) We prove that, under certain geometric conditions, that only \(m-1\) different non-degenerate \((m+2)\)-secant \(m\)-planes plus one degenerate \((m+2)\)-secant \(m\)-plane to the Kummer variety implies the existence of a curve of ${(m+2)}$-secants to the Kummer variety. This is done by constructing a set of equations in terms of theta functions from the germ of a curve on the described points. The relation between those equations allows to proceed by induction to get the entire desired curve since the first of them is equivalent to the hypothesis that we ask. |
| title | A Curve of Secants to the Kummer Variety from Degenerate Points |
| topic | Algebraic Geometry 14K25, 14H40 (Primary) |
| url | https://arxiv.org/abs/2603.12393 |