发表机构
University of Melbourne（墨尔本大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在旋量曲线模空间构建微分几何结构，推广双曲旋量结构与全纯层的关系，构造特征形式与旋量测度，发现旋量模空间奇偶分量体积贡献的对称性。
AI 中文摘要
本文源于在切特拉罗举办的CIME暑期学校迷你课程讲义，我们在光滑旋量曲线的模空间${\rm spin}_{g,n}$上构建微分几何结构，特别强调其在双曲几何中的解释。我们将双曲旋量结构产生的局部常值层与对应全纯层关联，把这一已知关系推广至带有Ramond标记点的旋量曲线。我们利用双曲描述，在带测地线边界的双曲曲面模空间上构造特征形式与旋量测度，为将Teichmüller理论方法应用于其体积及体积递推提供框架。最后，我们分别研究旋量模空间的偶分量与奇分量，发现它们体积贡献间存在对称性，该对称性在各边界层的贡献中并不明显。
英文摘要
This article arose out of notes for a CIME summer school mini-course in Cetraro. In it we develop differential-geometric constructions on the moduli space ${\cal M}_{g,n}^{\rm spin}$ of smooth spin curves, with particular emphasis on their interpretation in hyperbolic geometry. We relate the locally constant sheaf arising from a hyperbolic spin structure to the corresponding holomorphic sheaf, extending this known relationship to spin curves with Ramond marked points. We use the hyperbolic description to construct characteristic forms and spin measures on moduli spaces of hyperbolic surfaces with geodesic boundary, providing a framework for applying Teichmüller-theoretic methods to their volumes and volume recursions. Finally, we study separately the even and odd components of spin moduli space and find symmetries between their volume contributions which are not apparent from the contributions of individual boundary strata.
Comments42 pages
