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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…
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…