We study a compactification of the moduli space of theta characteristics, giving a modular interpretation of the geometric points and describing the boundary stratification. This space is different from the moduli space of spin curves. The modular description and the boundary stratification of the new compactification are encoded by a tropical moduli space. We show that this tropical moduli space is a refinement of the moduli space of spin tropical curves. We describe explicitly the induced decomposition of its cones.

中文翻译：

---

准稳态自旋曲线的模空间

我们研究了 theta 特征的模空间的紧化，给出了几何点的模块化解释并描述了边界分层。这个空间不同于自旋曲线的模空间。新紧化的模块化描述和边界分层由热带模空间编码。我们表明，这个热带模空间是自旋热带曲线模空间的改进。我们明确描述了其视锥细胞的诱导分解。