复幂零流形的Teichmüller与模空间
Teichmüller and moduli spaces for complex nilmanifolds
- Philipps-Universität Marburg（马尔堡菲利普斯大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文为复幂零流形发展研究工具，证明全纯映射结构定理并引入周期映射，给出复结构存在判据，证明多类幂零流形的整体Torelli定理，并展示任意维数及幂零指数下Teichmüller空间可为复流形。
中文摘要 AI 辅助
我们发展了若干工具来研究复幂零流形的Teichmüller空间和模空间的局部与整体结构。作为起点，我们证明了复幂零流形之间全纯映射的一个结构定理，这使得能够显式描述Teichmüller空间和模空间。随后我们引入两个周期映射，并给出这些空间上存在复结构的一般判据。为阐释该理论，我们证明了若干类幂零流形的整体Torelli定理，包括环面上的主环丛和几乎阿贝尔幂零流形。特别地，我们表明存在任意维数和幂零指数的幂零流形，其Teichmüller空间具有复流形结构。
英文摘要
We develop several tools to study the local and global structure of the Teichmüller and moduli spaces for complex nilmanifolds. As a starting point, we prove a structure theorem for holomorphic maps between complex nilmanifolds, which allows for an explicit description of the Teichmüller and moduli spaces. We then introduce two period maps, and give general criteria for the existence of a complex structure on these spaces. To illustrate the theory, we prove a global Torelli theorem for various classes of nilmanifolds, including principal torus bundles over tori and almost abelian nilmanifolds. In particular, we show that there are nilmanifolds of arbitrary dimension and nilpotency index for which the Teichmüller space admits the structure of a complex manifold.
