AI 中文总结
该文研究平展二重覆盖的Prym簇上几何起源伪反射，证明g≥4时此类伪反射阶为2，推出g≥5时对应非平凡有限群仅为ℤ/2ℤ或(ℤ/2ℤ)²（后者仅g≤7时存在），改进了已有结果。
AI 中文摘要
我们研究平展二重覆盖的Prym簇上几何起源的伪反射，证明若基曲线的亏格g≥4，则每个此类伪反射的阶均为2。利用该结果可推出，当g≥5时，在Prym簇P上忠实作用且P/G光滑的非平凡几何起源自同构有限群G必同构于ℤ/2ℤ或(ℤ/2ℤ)²，且后者仅在g≤7时出现，这改进了Auff、Lahoz和Naranjo的相关结果。
英文摘要
We study pseudoreflections of geometric origin on Prym varieties of étale 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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