Abstract

The minimal stratum in Prym loci have been the first source of infinitely many primitive, but not algebraically primitive Teichmüller curves. We show that the stratum Prym(1, 2) contains no such Teichmüller curve and the stratum Prym(2) at most 92 such Teichmüller curves. This complements the recent progress establishing general – but non-effective – methods to prove finiteness results for Teichmüller curves and serves as proof of concept how to use the torsion condition in the non-algebraically primitive case.

中文翻译：

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Prym Loci 中 Teichmüller 曲线的不存在性和有限性结果

摘要

Prym 轨迹中的最小层是无限多原始但不是代数原始 Teichmüller 曲线的第一个来源。我们证明地层 Prym(1, 2) 不包含这样的 Teichmüller 曲线，而地层 Prym(2) 最多包含 92 条这样的 Teichmüller 曲线。这补充了最近建立一般但无效的方法来证明 Teichmüller 曲线的有限性结果的进展，并作为如何在非代数原始情况下使用扭转条件的概念证明。