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arXiv · 2503.23041

Pryms of $\mathbb{Z}_3\times\mathbb{Z}_3$ coverings of genus 2 curves

Paweł Borówka·Anatoli Shatsila
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Abstract

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

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Paweł Borówka, Anatoli Shatsila. 2025-03-29. Pryms of $\mathbb{Z}_3\times\mathbb{Z}_3$ coverings of genus 2 curves. https://arxiv.org/abs/2503.23041

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