Torelli 群与曲线模空间几何
摘要
本文给出 Dennis Johnson 关于 Torelli 群第一 homology 研究的综述，并展示如何将其结果单独或与 Saito 的 Hodge 模块理论结合用于研究曲线模空间的几何。例如，我们证明了具有固定水平结构的曲线模空间的 Picard 群是有限生成的，分类了定义在具有固定水平结构的曲线模空间上的所有“自然”正规函数，也“计算”了在曲线模空间上同调平凡且在一般点上互离的循环之间的高度配对。添加了若干新章节，这些章节运用正规函数的结果，证明了古典 Franchetta 猜想在曲线和阿贝尔 variety 中的广义形式。在一个章节中，计算了 canonical bundle nth 根的 monodromy 群。
引用
@article{arxiv.alg-geom/9403015,
title = {Torelli Groups and Geometry of Moduli Spaces of Curves},
author = {Richard M. Hain},
journal= {arXiv preprint arXiv:alg-geom/9403015},
year = {2008}
}
备注
38 pages, AMS-LaTeX. Abstract of revised version: This is a significanly revised and expanded version of the original paper. Several significant typos in the section on heights have been corrected and four new sections have been added. Among the new results are proofs of several generalizations of the classical Franchetta Conjecture to curves with a level structure and n marked points. Another section contains a computation of the monodromy group of nth roots of the canonical bundle. The two