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| Format: | Preprint |
| Veröffentlicht: |
2021
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| Online-Zugang: | https://arxiv.org/abs/2103.12490 |
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| _version_ | 1866912096347750400 |
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| author | Lü, Xin Sun, Ruiran Zuo, Kang |
| author_facet | Lü, Xin Sun, Ruiran Zuo, Kang |
| contents | We introduce the notion of topological hyperbolicity to characterize the largeness of the topological fundamental group of a complex variety. Inspired by the Shafarevich conjecture, we propose to study the topological hyperbolicity of moduli spaces of polarized manifolds. We provide two pieces of supporting evidence: first, we show that moduli spaces where the infinitesimal Torelli theorem holds are very close to being topologically hyperbolic. Second, we establish a weak form of topological hyperbolicity for moduli spaces of elliptic surfaces of Kodaira dimension one without multiple fibers, where the infinitesimal Torelli theorem generally does not hold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_12490 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Topological Hyperbolicity of Moduli spaces of Elliptic Surfaces Lü, Xin Sun, Ruiran Zuo, Kang Algebraic Geometry Geometric Topology We introduce the notion of topological hyperbolicity to characterize the largeness of the topological fundamental group of a complex variety. Inspired by the Shafarevich conjecture, we propose to study the topological hyperbolicity of moduli spaces of polarized manifolds. We provide two pieces of supporting evidence: first, we show that moduli spaces where the infinitesimal Torelli theorem holds are very close to being topologically hyperbolic. Second, we establish a weak form of topological hyperbolicity for moduli spaces of elliptic surfaces of Kodaira dimension one without multiple fibers, where the infinitesimal Torelli theorem generally does not hold. |
| title | Topological Hyperbolicity of Moduli spaces of Elliptic Surfaces |
| topic | Algebraic Geometry Geometric Topology |
| url | https://arxiv.org/abs/2103.12490 |