A note on smooth quotients of Prym varieties

Anatoli Shatsila

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arXiv · 2608.18000

A note on smooth quotients of Prym varieties

Anatoli Shatsila

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Abstract

We study pseudoreflections of geometric origin on Prym varieties of \'etale double covers. We prove that if the genus of the base curve is $g \geq 4$ then every such pseudoreflection has order 2. We use this result to show that, for $g \geq 5$, a non-trivial finite group $G$ of automorphisms of geometric origin acting faithfully on the Prym $P$ with $P/G$ smooth must be isomorphic to either $\mathbb{Z}/2\mathbb{Z}$ or $(\mathbb{Z}/2\mathbb{Z})^2$. We also show that the latter case can occur only for $g \leq 7$. This sharpens results of Auffarth, Lahoz and Naranjo.

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Anatoli Shatsila. 2026-08-18. A note on smooth quotients of Prym varieties. https://arxiv.org/abs/2608.18000

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