Period differential equations for the families of K3 surfaces with two parameters derived from the reflexive polytopes

Atsuhira Nagano

doi:10.2206/kyushujm.66.193

Period differential equations for the families of K3 surfaces with two parameters derived from the reflexive polytopes

Atsuhira Nagano^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In this paper, we study the period mappings for the families of K3 surfaces derived from the three-dimensional reflexive polytopes with five vertices. We determine the lattice structures, the period differential equations and the projectivemonodromy groups.Moreover, we show that one of our period differential equations coincides with the uniformizing differential equation of the Hilbert modular orbifold for the field ℚ(√5).

Original language	English
Pages (from-to)	193-244
Number of pages	52
Journal	Kyushu Journal of Mathematics
Volume	66
Issue number	1
DOIs	https://doi.org/10.2206/kyushujm.66.193
Publication status	Published - 2012

Keywords

Hilbert modular orbifolds
K3 surfaces
Period differential equations
Period maps
Toric varieties

ASJC Scopus subject areas

Mathematics(all)

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10.2206/kyushujm.66.193

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abstract = "In this paper, we study the period mappings for the families of K3 surfaces derived from the three-dimensional reflexive polytopes with five vertices. We determine the lattice structures, the period differential equations and the projectivemonodromy groups.Moreover, we show that one of our period differential equations coincides with the uniformizing differential equation of the Hilbert modular orbifold for the field ℚ(√5).",

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AB - In this paper, we study the period mappings for the families of K3 surfaces derived from the three-dimensional reflexive polytopes with five vertices. We determine the lattice structures, the period differential equations and the projectivemonodromy groups.Moreover, we show that one of our period differential equations coincides with the uniformizing differential equation of the Hilbert modular orbifold for the field ℚ(√5).

KW - Hilbert modular orbifolds

KW - K3 surfaces

KW - Period differential equations

KW - Period maps

KW - Toric varieties

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Period differential equations for the families of K3 surfaces with two parameters derived from the reflexive polytopes

Abstract

Keywords

ASJC Scopus subject areas

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