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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/2506.02871 |
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| _version_ | 1866918044444393472 |
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| author | Biswas, Indranil Ghigi, Alessandro Vai, Luca |
| author_facet | Biswas, Indranil Ghigi, Alessandro Vai, Luca |
| contents | Given an étale double covering $π\, :\, \widetilde{C}\, \longrightarrow\, C$ of compact Riemannsurfaces with $C$ of genus at least two, we use the Prym variety of the cover to construct canonical projective structures on both $\widetilde C$ and $C$. This construction can be interpreted as a section of an affine bundle over the moduli space of étale double covers. The $\overline{\partial}$--derivative of this section is a (1,1)--form on the moduli space. We compute this derivative in terms of Thetanullwert maps. Using the Schottky--Jung identities we show that, in general, the projective structure on $C$ depends on the cover. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prym varieties and projective structures on Riemann surfaces Biswas, Indranil Ghigi, Alessandro Vai, Luca Algebraic Geometry Given an étale double covering $π\, :\, \widetilde{C}\, \longrightarrow\, C$ of compact Riemannsurfaces with $C$ of genus at least two, we use the Prym variety of the cover to construct canonical projective structures on both $\widetilde C$ and $C$. This construction can be interpreted as a section of an affine bundle over the moduli space of étale double covers. The $\overline{\partial}$--derivative of this section is a (1,1)--form on the moduli space. We compute this derivative in terms of Thetanullwert maps. Using the Schottky--Jung identities we show that, in general, the projective structure on $C$ depends on the cover. |
| title | Prym varieties and projective structures on Riemann surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2506.02871 |