Period differential equations for families of K3 surfaces derived from some 3 dimensional reflexive polytopes

2010/01/29 by Atsuhira Nagano, Nagano, Atsuhira
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #math.CV

paper · pdf · doi:10.48550/arxiv.1001.5312

The results of this paper are contained in "Period differential equations for the families of K3 surfaces with 2 parameters derived from the reflexive polytopes "

openalex publication_date 2010/01/29 · arxiv created 2016/03/29 · arxiv updated 2016/03/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study period maps for families of K3 surfaces those are given by anti canonical divisors of toric varieties coming from reflexive polytopes P₂, P₄, P₅ and P_r. We obtain systems of period differential equations for these families. Moreover, in the case P₄, we determine the projective monodromy group of the period map. This group is explicitly related with the Hilbert modular group for ℚ(√(5)).

Citations

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

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