Scholarlink

This paper has three principal goals: to survey what is known about mapping class and Torelli groups of simply connected compact Kähler manifolds, to supplement these results, and to present a list of questions and open problems to stimulate future work. Apart from reviewing general background, the paper focuses on the case of hypersurfaces in projective space. We explain how older results of Carlson–Toledo and recent results of Kreck–Su imply that the homomorphism from the fundamental group of the moduli space of hypersurfaces of degree at least 3 in \({\mathbb P}^4\) to the mapping class group of the underlying manifold has a very large kernel (for example, it contains a free group of rank 2) and has image of infinite index. This is in contrast to the case of curves, where the homomorphism is an isomorphism.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Mapping Class Groups of Simply Connected Kähler Manifolds

  • 会议论文

  • 发表日期：

    2025年

查看全文
  • Richard Hain

摘要

This paper has three principal goals: to survey what is known about mapping class and Torelli groups of simply connected compact Kähler manifolds, to supplement these results, and to present a list of questions and open problems to stimulate future work. Apart from reviewing general background, the paper focuses on the case of hypersurfaces in projective space. We explain how older results of Carlson–Toledo and recent results of Kreck–Su imply that the homomorphism from the fundamental group of the moduli space of hypersurfaces of degree at least 3 in \({\mathbb P}^4\) to the mapping class group of the underlying manifold has a very large kernel (for example, it contains a free group of rank 2) and has image of infinite index. This is in contrast to the case of curves, where the homomorphism is an isomorphism.