The Complex Ball-quotient Structure of the Moduli Space of Certain Sextic Curves

2021/10/20 by Zhiwei Zheng, Yiming Zhong, Zheng, Zhiwei +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2110.10630

openalex publication_date 2021/10/20 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28

Abstract

We study moduli spaces of certain sextic curves with a singularity of multiplicity 3 from both perspectives of Deligne-Mostow theory and periods of K3 surfaces. In both ways we can describe the moduli spaces via arithmetic quotients of complex hyperbolic balls. We show in Theorem 7.4 that the two ball-quotient constructions can be unified in a geometric way.

Citations

• Moduli of Nodal Sextic Curves via Periods of K3 Surfaces

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