Characterization of Beauville's algebraic numbers via Hodge theory

2020/09/30 by Muxi Li, Mao Sheng, Li, Muxi +1
Mathematics · #14D07 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2009.14529

openalex publication_date 2020/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℙ¹ with four singular fibers. Our technical innovation is the analysis of the periodicity of the uniformizing Higgs bundle attached to ℙ¹ minus four points over the field of complex numbers.

Related

• Betti and Hodge numbers of configuration spaces of a punctured elliptic curve from its zeta functions
• Wild nonabelian Hodge theory on curves
• Counting Higgs bundles
• The arithmetic Hodge index theorem for adelic line bundles I
• Hodge polynomials of the SL(2,C)-character variety of an elliptic curve with two marked points