A period differential equation for a family of K3 surfaces and the Hilbert modular orbifold for the field ℚ(√(5))

2010/09/29 by Atsuhira Nagano, Nagano, Atsuhira · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1009.5725

openalex publication_date 2010/09/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this article we study the period map for a family of K3 surfaces which is given by the anticanonial divisor of a toric variety. We determine the period differential equation and its monodromy group. Moreover we show the exact relation between our period differential equation and the unifomizing differential equation of the Hilbert modular orbifold for the field ℚ(√(5)).

Citations

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

Cited by

• Period differential equations for families of K3 surfaces derived from 3 dimensional reflexive polytopes with 5 vertices

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