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Autori principali: Lü, Xin, Sun, Ruiran, Zuo, Kang
Natura: Preprint
Pubblicazione: 2021
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Accesso online:https://arxiv.org/abs/2103.12490
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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