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arXiv · 2103.12490

Topological Hyperbolicity of Moduli spaces of Elliptic Surfaces

Xin Lü·Ruiran Sun·Kang Zuo
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Abstract

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.

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Xin Lü, Ruiran Sun, Kang Zuo. 2021-03-23. Topological Hyperbolicity of Moduli spaces of Elliptic Surfaces. https://arxiv.org/abs/2103.12490

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