Modular surfaces associated with toric K3 hypersurfaces
  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. 
Kenji Hashimoto, Atsuhira Nagano, Kazushi Ueda
math.AG