Characterization of Beauville’s Numbers via Hodge Theory

DOI10.1093/IMRN/RNAB211zbMATH Open1503.14029arXiv2009.14529OpenAlexW3192108677WikidataQ114092329 ScholiaQ114092329MaRDI QIDQ5047079

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Publication date: 9 November 2022

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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.

Full work available at URL: https://arxiv.org/abs/2009.14529

zbMATH Keywords

elliptic curvesHiggs bundleHodge theorysingular fibersBeauville's numbers

Mathematics Subject Classification ID

Fibrations, degenerations in algebraic geometry (14D06) de Rham cohomology and algebraic geometry (14F40) Vector bundles on curves and their moduli (14H60) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30)

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