Modular surfaces associated with toric K3 hypersurfaces

Abstract

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, and the other is related to the product of modular curves.

arXiv comment25 pages, 15 figures

References in corpus (5)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• An integral structure in quantum cohomology and mirror symmetry for toric orbifolds
• Identities between Appell's and hypergeometric functions
• Compact moduli of hyperplane arrangements
• Period differential equations for the families of $K3$ surfaces with $2$ parameters derived from the reflexive polytopes

Cited by in corpus (2)

• Mirror symmetry and K3 surfaces
• Icosahedral invariants and Shimura curves