Pryms of $\mathbb{Z}_3\times\mathbb{Z}_3$ coverings of genus 2 curves
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912916719009792 |
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| author | Borówka, Paweł Shatsila, Anatoli |
| author_facet | Borówka, Paweł Shatsila, Anatoli |
| contents | We study unramified Galois $\mathbb{Z}_3 \times \mathbb{Z}_3$ coverings of genus 2 curves and the corresponding Prym varieties and Prym maps. In particular, we prove that any such covering can be reconstructed from its Prym variety, that is, the Prym-Torelli theorem holds for these coverings. We also investigate the Prym map of unramified $G$-coverings of genus 2 curves for an arbitrary abelian group $G$. We show that the generic fiber of the Prym map is finite unless $G$ is cyclic of order less than 6 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23041 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pryms of $\mathbb{Z}_3\times\mathbb{Z}_3$ coverings of genus 2 curves Borówka, Paweł Shatsila, Anatoli Algebraic Geometry 14H40, 14H30, 14H45, 14K12 We study unramified Galois $\mathbb{Z}_3 \times \mathbb{Z}_3$ coverings of genus 2 curves and the corresponding Prym varieties and Prym maps. In particular, we prove that any such covering can be reconstructed from its Prym variety, that is, the Prym-Torelli theorem holds for these coverings. We also investigate the Prym map of unramified $G$-coverings of genus 2 curves for an arbitrary abelian group $G$. We show that the generic fiber of the Prym map is finite unless $G$ is cyclic of order less than 6 |
| title | Pryms of $\mathbb{Z}_3\times\mathbb{Z}_3$ coverings of genus 2 curves |
| topic | Algebraic Geometry 14H40, 14H30, 14H45, 14K12 |
| url | https://arxiv.org/abs/2503.23041 |