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

Research output: Contribution to journal › Article

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

Fingerprint

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

Cite this

Nagano, A. (2012). Period differential equations for the families of K3 surfaces with two parameters derived from the reflexive polytopes. Kyushu Journal of Mathematics, 66(1), 193-244. https://doi.org/10.2206/kyushujm.66.193

@article{3d2ed708f5a94f0eaa11cf9b537791c9,

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

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).",

keywords = "Hilbert modular orbifolds, K3 surfaces, Period differential equations, Period maps, Toric varieties",

author = "Atsuhira Nagano",

year = "2012",

doi = "10.2206/kyushujm.66.193",

language = "English",

volume = "66",

pages = "193--244",

journal = "Kyushu Journal of Mathematics",

issn = "1340-6116",

publisher = "Kyushu University, Faculty of Science",

number = "1",

}

TY - JOUR

T1 - Period differential equations for the families of K3 surfaces with two parameters derived from the reflexive polytopes

AU - Nagano, Atsuhira

PY - 2012

Y1 - 2012

N2 - 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).

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

UR - http://www.scopus.com/inward/record.url?scp=84870882842&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870882842&partnerID=8YFLogxK

U2 - 10.2206/kyushujm.66.193

DO - 10.2206/kyushujm.66.193

M3 - Article

AN - SCOPUS:84870882842

VL - 66

SP - 193

EP - 244

JO - Kyushu Journal of Mathematics

JF - Kyushu Journal of Mathematics

SN - 1340-6116

IS - 1

ER -

Access to Document

10.2206/kyushujm.66.193