10 citations · 44 across the 19 of their papers we have counts for
20 papers
Picard-Fuchs system for family of Kummer surfaces as subsystem of GKZ hypergeometric system
Atsuhira Nagano
We determine a simple expression of the Picard-Fuchs system for a family of Kummer surfaces for all principally polarized Abelian surfaces. It is given by a system of linear partia…
On Riemann type relations for theta functions on bounded symmetric domains of type
Atsuhira Nagano
We provide a practical technique to obtain plenty of algebraic relations for theta functions on the bounded symmetric domains of type . In our framework, each theta relation is…
Elliptic fibrations on toric hypersurfaces and mirror symmetry derived from Fano polytopes
Tomonao Matsumura, Atsuhira Nagano
We determine the Néron-Severi lattices of hypersurfaces with large Picard number in toric three-folds derived from Fano polytopes. On each surface, we introduce a particu…
Sequence of families of lattice polarized surfaces, modular forms and degrees of complex reflection groups
Atsuhira Nagano
We introduce a sequence of families of lattice polarized surfaces. This sequence is closely related to complex reflection groups of exceptional type. Namely, we obtain modular…
The ring of modular forms for the even unimodular lattice of signature (2,18)
Atsuhira Nagano, Kazushi Ueda
We show that the ring of modular forms with characters for the even unimodular lattice of signature (2,18) is obtained from the invariant ring of $\mathrm{Sym}(\mathrm{Sym}^8(V) \o…
On Kummer-like surfaces attached to singularity and modular forms
Atsuhira Nagano, Hironori Shiga
We study a family of lattice polarized surfaces which is an extension of the family of Kummer surfaces derived from principally polarized Abelian surfaces. Our family has two…
The ring of modular forms of with characters
Atsuhira Nagano, Kazushi Ueda
We show that the ring of modular forms with characters for is generated by forms of weights 4, 4, 6, 8, 10, 10, 12, and 30 with three relations of weig…
Geometric interpretation of Hermitian modular forms via Burkhardt invariants
Atsuhira Nagano, Hironori Shiga
We give a complete theta expression of a pair of Hermitian modular forms as an inverse period mapping of lattice polarized surfaces. Our result gives a non-trivial relation am…
Inverse period mappings of surfaces and a construction of modular forms for a lattice with the Kneser conditions
Atsuhira Nagano
We explicitly construct modular forms on a -dimensional bounded symmetric domain of type based on the variation of the Hodge structures of surfaces. We study the ring…
On rings of differential operators derived from automorphic forms
Atsuhira Nagano
We study linear ordinary differential equations which are analytically parametrized on Hermitian symmetric spaces and invariant under the action of symplectic groups. They are gene…
A theta expression of the Hilbert modular functions for via the periods of surfaces
Atsuhira Nagano
In this paper, we give an extension of the classical story of the elliptic modular function to the Hilbert modular case for . We construct the period mapping…
Double integrals on a weighted projective plane and the Hilbert modular functions for
Atsuhira Nagano
The aim of this paper is to give an explicit extension of the classical elliptic integrals to the Hilbert modular case for . We study a family of Kummer surfa…
Period differential equations for the families of surfaces with parameters derived from the reflexive polytopes
Atsuhira Nagano
In this paper, we study the period mappings for the families of surfaces derived from the -dimensional -verticed reflexive polytopes. We determine the lattice structures…
To the Hilbert class field from the hypergeometric modular function
Atsuhira Nagano, Hironori Shiga
In this article we make an explicit approach to the higher degree case of the problem: " For a given field , construct its maximal abelian extension (i.e. the Hilber…
Icosahedral invariants and a construction of class fields via periods of surfaces
Atsuhira Nagano
In the theory of complex multiplication, it is important to construct class fields over CM fields. In this paper, we consider explicit surfaces parametrized by Klein's icosahe…
Icosahedral invariants and Shimura curves
Atsuhira Nagano
Shimura curves are moduli spaces of abelian surfaces with quaternion multiplication. Models of Shimura curves are very important in number theory. Klein's icosahedral invariants $\…
Modular surfaces associated with toric K3 hypersurfaces
Kenji Hashimoto, Atsuhira Nagano, Kazushi Ueda
We give detailed descriptions of the period maps of two 2-parameter families of anti-canonical hypersurfaces in toric 3-folds. One of them is related to a Hilbert modular surface,…
Period differential equations for families of surfaces derived from 3 dimensional reflexive polytopes with 5 vertices
Atsuhira Nagano
In this article we study the families of surfaces derived from 3 dimensional 5 verticed reflexive polytopes with at most terminal singularity. We determine the lattice structu…
A period differential equation for a family of surfaces and the Hilbert modular orbifold for the field
Atsuhira Nagano
In this article we study the period map for a family of surfaces which is given by the anticanonial divisor of a toric variety. We determine the period differential equation a…
Period differential equations for families of K3 surfaces derived from some 3 dimensional reflexive polytopes
Atsuhira Nagano
We study period maps for families of surfaces those are given by anti canonical divisors of toric varieties coming from reflexive polytopes and . We obtai…