Inversion of the Abel--Prym map for real curves with involutions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912986067632128 |
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| author | Sheinman, Oleg K. |
| author_facet | Sheinman, Oleg K. |
| contents | Riemann vanishing theorem is a main ingredient of the conventional technique related to the Jacobi inversion problem. In the case of curves with a holomorphic involution, it has been presented quite fully in wellknown Fay's Lectures on theta functions. The case of real algebraic curves with involution is presented with less completeness in the literature. We provide a detailed presentation of that case, including the case of real curves of the non-separating type with a holomorphic involution, not considered before with this relation. In particular, we formulate the symmetry of the Prym theta function in this case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_04229 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inversion of the Abel--Prym map for real curves with involutions Sheinman, Oleg K. Algebraic Geometry Mathematical Physics Riemann vanishing theorem is a main ingredient of the conventional technique related to the Jacobi inversion problem. In the case of curves with a holomorphic involution, it has been presented quite fully in wellknown Fay's Lectures on theta functions. The case of real algebraic curves with involution is presented with less completeness in the literature. We provide a detailed presentation of that case, including the case of real curves of the non-separating type with a holomorphic involution, not considered before with this relation. In particular, we formulate the symmetry of the Prym theta function in this case. |
| title | Inversion of the Abel--Prym map for real curves with involutions |
| topic | Algebraic Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2511.04229 |