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arXiv · 2009.14529

Characterization of Beauville's algebraic numbers via Hodge theory

Muxi Li·Mao Sheng
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Abstract

We provide a Hodge theoretical characterization of the set of algebraic numbers which arises from the complete list, due to A. Beauville, of semistable families of elliptic curves over $\mathbb{P}^1$ with four singular fibers. Our technical innovation is the analysis of the periodicity of the uniformizing Higgs bundle attached to $\mathbb{P}^1$ minus four points over the field of complex numbers.

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Muxi Li, Mao Sheng. 2020-09-30. Characterization of Beauville's algebraic numbers via Hodge theory. https://arxiv.org/abs/2009.14529

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